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I like to use a two step method for finding the inverse of a function:
Step 1: Interchange the x and y. Once you interchange the variables, this y becomes the y that represents

Step 2: Solve for y.

Begin by writing this f(x) in notation of y:



Step 1:



Step 2:


Clear fractions:






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log(x) + log(x+15) = 2


Use the first law of logarithms to form a single logarithm:


Using the basic definition, convert to exponential form:




Solve the quadratic formula by factoring if possible, otherwise the quadratic formula or completing the square:
(Isn't it nice when these kinds of problems factor? )
or

You must check these answers to make sure that none of the values of x make a log of a negative (logs of negatives are not allowed in the real numbers!!). Therefore, the answer must be rejected.

The final answer is .

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The graph of y=x^2 is a parabola that opens upward. Therefore, is that same parabola that opens upward, but it is moved UP one unit. It looks like this:


A graph is increasing if when you move along the graph from LEFT to RIGHT, the y value becomes larger, and it is decreasing if when you move from LEFT to RIGHT the y value becomes smaller. From looking at the graph, notice that the graph is DECREASING on the left side of the graph, and INCREASING on the right side of the graph. Therefore, it is DECREASING from -infinity to x=0, and it is INCREASING from x=0 to infinity.

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Let x= number of kilometers traveled
Then the total cost of the taxi is
8+3x = 83
8+3x -8 = 83-8
3x=75
x= 25 kilometers

By the way, I am from the USA where we use $. What is an R???

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Sanford, FL USA

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Area of a circle = . Is that what you wanted???

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In order to add two fractions, you must first find the Least Common Denominator (LCD). In this case, the LCD =

In order to get the LCD in the first fraction, you must multiply the numerator and denominator of this first fraction by all the missing factors, which would be . In the second fraction, the missing factors are only .

It should look like this:





I just noticed that we could have reduced the second fraction FIRST, which would have made this easier. However, you can reduce the answer now by factoring the numerator:


Divide out the factors of 2:

------------------------------------------------------------------------------------
Here is what it looks like if you reduce the fraction FIRST:



Now the LCD=




I don't know!! It's very late in Central Florida, USA, and I may have made a errors on this problem. If you find any, please let me know!! If you need more help with LCD problems, click on my tutor name "rapaljer", go to "MATH IN LIVING COLOR" and look for Basic Algebra, Chapter 3.

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In order to find the equation of a line, you must know two things:
1) Slope
2) Y-intercept

In this problem, the slope must be found by writing the given equation in "slope-intercept" form. That is, you must solve for y in terms of x.
3x+5y=15
5y = -3x + 15

Divide both sides by 5:



The slope of the given line is m=-3/5, so the slope of any line PARALLEL to this line is also m=-3/5.

Secondly, the given point (0,9) just happens to be the Y-intercept, so in the equation
y=mx+b
m=-3/5 and b=9


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You will have to give us the problems, since we don't have your book.
---OR---
Check out MY book, portions of which are explained "IN LIVING COLOR". Click on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", then click on either Basic or Intermediate Algebra, Chapter 2. Look at all these factoring topics. You may find what you need there.

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Anytime there are four terms in a factoring problem, first try grouping the first two and the last two terms together:
2xy - 4x + 3y - 6
From the first two terms take out a common factor of 2x, from the second two terms take out a 3 factor:

2xy - 4x + 3y - 6
2x(y - 2) + 3(y - 2)

Notice the common factor of (y-2):
(y-2)(2x-3)

For additional help with factoring, see my Lesson Plans in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", then look in either Basic or Intermediate Algebra for "Chapter 2," then "Factoring the Common Factor."

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Let x = shortest side (a leg of the right triangle)
x+3 = longer side (a leg of the right triangle)
= longest side (hypotenuse of right triangle)





Set equal to zero, moving everything to the right side of the equation:



This does NOT factor (does this have an ugly answer??), so you'll have to complete the square or use the quadratic formula. I will complete the square:







Reject the negative answer, since a side of a triangle cannot be negative:
meters (shortest side)
meters (second leg of the right triangle)
meters (hypotenuse)
meters (hypotenuse)

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You are correct in your set up of the problem:
Woman= h+5
Husband= h
Daughter=(h+5)/10

However, the equation has to do with the sum of their ages in 14 years. These are the ages in 14 years:

Woman= h+5 +14
Husband= h +14
Daughter=(h+5)/10 + 14

The equation should be:
(h+5)+14 +(h)+14 +((h+5)/10)+14 =100

Subtract 14*3 = 42 from each side, and your equation will equal 58 instead of 100. Try that and see if it works. I think you may have had another error as well:
(h+5) +(h) +((h+5)/10) =58
2h+5 + (h+5)/10 = 58
20h + 50 + h+5 = 580
21h + 55 = 580
21h = 525
h= 525/21 = 25 years old = Husband
w = 30 years old = Wife
d = 30/10= 3 years old = Daughter

In 14 years:
Husband will be 39
Wife will be 44
Daughter will be 17

Check: 39+44+17= 100 years young!!

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Translated to exponential notation, this means


Indeed, since ,

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(NOTE: is NOT a valid solution, since you can't have a log of a negative number!)

Final answer:

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Don't you mean i = radical -1??? And therefore,

Anyway,




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N=F+d(n-1)

Perhaps you mean to solve for lower case n! It is very important to realize that in math, when upper case and lower case letters are used in an equation, they represent DIFFERENT variables. If you really wanted to solve for capital N, then the given equation does that already. However, assuming that you want to solve for "n", first remove the parentheses by distributive property:
N= F+ dn - d

Next, get all the NON-"n" terms on the left side, and get the "n" term (that is, "dn") by itself. You can do this by subtracting F and adding d to each side:

N= F+ dn - d
N-F +d = F+dn-d -F +d
N-F + d = dn

Next, divide both sides by d, so as to "undo" the multiplication of d times n:



Resist the temptation to reduce this expression by dividing out the d's! You NEVER DIVIDE OUT TERMS!!!

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This is a difference of two squares, which factors like this:
(First-Second)*(First + Second)




If you need more help, please see my Lesson Plans in algebra.com on Factoring the Difference of Squares, or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", then go to Chapter 2 of either Basic Algebra or Intermediate Algebra.

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I was RIGHT!! This is the way the problem could have been stated:
over

When you raise a power to a power, you MULTIPLY exponents! (By the way, if you need help with the Laws of Exponents, please see my Lesson Plan on algebra.com, or go to my own website by clicking on my tutor name "rapaljer", then look for "MATH IN LIVING COLOR," then "Basic Algebra", then Chapter 2.)

over

When you divide, you must SUBTRACT exponents:
over



When you divide, again you SUBTRACT exponents:


When you have a negative exponent, this means

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I can't tell from your description what x is. Maybe you should resubmit the question.

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You can start by factoring out the common factor of 2:


This trinomial just happens to factor:

There are two solutions:
2x-1=0
2x=1


x-1=0
x=1

If you need more help solving quadratic equations by factoring, see my Lesson Plans in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for "Math in Living Color", then look in Basic Algebra or Intermediate Algebra, Chapter 2 for the topic "Solving Quadratic Equations".

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You just multiply the number of people times the amount of water per person:
L
L
L
L

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Introductory note: On this problem, you really have to watch your p's and q's!!!






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Revenue = (Selling Price per item) * (Number of items sold)
Revenue =
Revenue =

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The Distributive Property is MULTIPLICATION OVER a SUM or DIFFERENCE! That is, there must be a multiplication and within parentheses, you MUST have either a sum or difference. In this case, the third answer does NOT meet these conditions:

g) 5(2*33) is NOT distributive property!

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A trinomial like this usually factors into the product of two binomials. The trick is to find two numbers whose product is the last number (in this case 24!) and whose sum (or difference!) is the middle number (in this case 25!). The answer to these questions is 24 times 1, so the answer is


For more help on this topic, see my Lesson Plans on Factoring Trinomials in algebra.com, or visit my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", then look for topics relating to "Factoring", which would be in Chapter 2 of Basic Algebra, or Chapter 2 of Intermediate Algebra.

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Was there more information given in this problem? Were you looking for the value of a where the function is undefined? Were you looking for the value of a that gives a particular value of f(x)? I don't think the question can be answered without more information.

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You are correct, . Now if volume is 1000 cm^3, then




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It looks right to me!!!

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First draw a horizontal line at y = -3. Make this a SOLID line. Then since this is y<= -3, shade everything BELOW the line:
.
You will have to shade the graph yourself, since I don't know how to do shade the region in algebra.com.

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First draw a horizontal line at y = -3. Make this a SOLID line. Then since this is y<= -3, shade everything BELOW the line:
.
You will have to shade the graph yourself, since I don't know how to do shade the region in algebra.com.

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I'm not sure exactly what you want to do with this. First, it is not an equation. Second, did you want to multiply the two trinomials? If so, then this is what you should do:
(5x^4-2x^2+1)(x^2-5x+3)
= 5x^4(x^2-5x+3) -2x^2(x^2-5x+3) +1(x^2-5x+3)
= 5x^6 -25x^5 +15x^4 -2x^4 +10x^3 -6x^2 + x^2-5x+3

Finally, combine like terms:
= 5x^6 -25x^5 +13x^4 +10x^3 -5x^2 -5x+3

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f(x)=-2x+7

This is the graph of a straight line whose y intercept is 7 and whose slope is -2. There are several ways to graph it, but it should look like this:


For your second question:
if f(x)=4x-3 find f(-1). This means that x=-1, so substitute this for x:
f(-1) =4(-1) -3
f(-1)=-7

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