Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

Tutors Answer Your Questions about Functions (FREE)

Question 1208224: 1. If f(x)=2x-6, what is f(7)-9
2. If G(x)=x-2x^2, what is g(-3)+13
Click here to see answer by josgarithmetic(39613)

Question 1208224: 1. If f(x)=2x-6, what is f(7)-9
2. If G(x)=x-2x^2, what is g(-3)+13
Click here to see answer by timofer(104)

Question 1208300: Given W(x)=3(2x-4),what is w(5)?
Click here to see answer by ikleyn(52750)

Question 1208404: 1. Find the domain of the expression x/(x^2 - 9).
x^2 - 9 = 0
x^2 = 9
sqrtx^2} = sqrt{9}
x = -3, and x = 3.
Domain = {x | x cannot be -3 and 3}.

2. Find the domain of the expression
(-9x^2 - x + 1)/(x^3 + x).
x^3 + x =
x(x^2 + 1) = 0
Setting x^2 + 1 to zero and solving for x leads to complex roots. I will disregard complex roots for now. The only value that x cannot be is 0.
Domain = {x | x cannot be 0}
What do y I say?

Click here to see answer by math_tutor2020(3816)

Question 1208403: 1. Find the domain of the expression (x^2 - 1)/x.
Domain = {x | x cannot be 0}.
2. Find domain of the expression x/(x^2 + 9).
The domain for question 2 does not exist over the real numbers. In later chapters, the idea of complex numbers is talked about. I say domain does not exist.
You say?
Click here to see answer by ikleyn(52750)

Question 1208460: Determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = x + 1 + 1/x
I already found this function is neither even nor odd, but I need help with the other parts.
Click here to see answer by ikleyn(52750)

Question 1208458: Determine this function is increasing, decreasing, even, odd, and/or invertible on its natural domain
.
I think I've already found that this is odd, because f(-x) = (-x)/((-x)^2+1) is clearly also equal to -f(x) = -x/(x^2 + 1), but I have having trouble finding whether this is increasing or decreasing.
I know:
increasing is when the gradient of the tangent is positive
and decreasing is when the gradient of the tangent is negative, but I need help finding this.
I am also already pretty sure there is no inverse.

Click here to see answer by Edwin McCravy(20054)

Question 1208750: Find the domain of y = sqrt{| x + 2|}.
Note: | x + 2 | means the absolute value of x plus 2.
Click here to see answer by ikleyn(52750)

Question 1208749: Find the domain of y = sqrt{4^(x + 4)}.

Click here to see answer by ikleyn(52750)

Question 1208748: Find the domain of y = x^(x).
Click here to see answer by ikleyn(52750)

Question 1208748: Find the domain of y = x^(x).
Click here to see answer by math_tutor2020(3816)

Question 1208803: Let f(x) and g(x) be functions. Find c if
(f \circ g)(x) = (g \circ f)(x)
for all x, where f(x) = 3x - 4 and g(x) = 5x + c.
Click here to see answer by math_tutor2020(3816)

Question 1208807: Question 1
(a) Write the function f(x) = 2x ^ 2 - 7x - 10 where x ∈ R, in the form a * (x + h) ^ 2 + k_{i} where a, h, and k \in
Qb) Hence, write the minimum point of f
(c) (i) Explain why / must have two real roots.
(ii) Write the roots of f(x) = 0 in the form p plus/minus sqrt(q) where p and q \in \mathbb{Q}
Click here to see answer by josgarithmetic(39613)

Question 1209281: The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.)
The parabola passes through (-5,-13), (2,7), and (4,-5).
Click here to see answer by greenestamps(13195)

Question 1209311: Let
f(x) = (2x + 3)/(x - 7) + sqrt(-x) + 1/(x^2 - 4).
Find the domain of f. Give your answer using interval notation.
Click here to see answer by greenestamps(13195)

Question 1209311: Let
f(x) = (2x + 3)/(x - 7) + sqrt(-x) + 1/(x^2 - 4).
Find the domain of f. Give your answer using interval notation.
Click here to see answer by math_tutor2020(3816)

Question 1209310: The function f satisfies
f(\sqrt{2x - 1}) = \frac{1}{2x - 1}
for all x not equal to 1/2. Find f(2).
Click here to see answer by ikleyn(52750)

Question 1209310: The function f satisfies
f(\sqrt{2x - 1}) = \frac{1}{2x - 1}
for all x not equal to 1/2. Find f(2).
Click here to see answer by math_tutor2020(3816)

Question 1209317: Let f be a function such that
f(x+y) = x + f(y) + f(y^2) - y^2
for any two real numbers x and y. If f(0) = -5, then what is f(1)?
Click here to see answer by Edwin McCravy(20054)

Question 1209317: Let f be a function such that
f(x+y) = x + f(y) + f(y^2) - y^2
for any two real numbers x and y. If f(0) = -5, then what is f(1)?
Click here to see answer by mccravyedwin(405)

Question 1197579: The price - demand equation and the costfunction for the production of
honey is given, respectively, by
x = 5,000 - 100p and C(x) = 2,500 + 4x+ 0.01x2
where x is the number of bottles that can be sold at a price of $p per
bottle and C(x) is the total cost (in dollars) of producing x bottles.
a) Express the price p as a function of the demand x, and find the domain of
this function.
b) Find the marginal cost.
c) Find the revenue function and state its domain.
d) Find the marginal revenue.
e) Find R′(2,000) and R′(3,000) and interpret these quantities.
f) Find the profit function in terms of x.
g) Find the marginal profit.
h) Find P′(1,000) and P′(1,500) and interpret these quantities.
Click here to see answer by onyulee(41)

Question 1209327: Let
f(x) = (2x + 5)/(x - 4).
If f^{-1} is the inverse of f, what is f^{-1}(1)?
Click here to see answer by mccravyedwin(405)

Question 1209327: Let
f(x) = (2x + 5)/(x - 4).
If f^{-1} is the inverse of f, what is f^{-1}(1)?
Click here to see answer by ikleyn(52750)

Question 1209327: Let
f(x) = (2x + 5)/(x - 4).
If f^{-1} is the inverse of f, what is f^{-1}(1)?
Click here to see answer by greenestamps(13195)

Question 1209327: Let
f(x) = (2x + 5)/(x - 4).
If f^{-1} is the inverse of f, what is f^{-1}(1)?
Click here to see answer by math_tutor2020(3816)

Question 1209328: Let f(x) and g(x) be functions. Find c if
(f \circ g)(x) = (g \circ f)(x)
for all x, where f(x) = 3x - 4 and g(x) = x + c.
Click here to see answer by mccravyedwin(405)

Question 1209325: Let x spadesuit y = x^2/y for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that a spadesuit a + 1 = 9. Write your answer as a list separated by commas.
Click here to see answer by ikleyn(52750)

Question 1209326: Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2.
Click here to see answer by ikleyn(52750)

Question 1209343: The graph of the exponential function f(x) is shown below. Find f(x).
The graph passes through the points (0,3) and (1,6).
Click here to see answer by mccravyedwin(405)

Question 1209343: The graph of the exponential function f(x) is shown below. Find f(x).
The graph passes through the points (0,3) and (1,6).
Click here to see answer by math_tutor2020(3816)

Question 1209413: The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).
Explain why the functions f and h are not the same function.
Click here to see answer by ikleyn(52750)

Question 1192280: Suppose f(x) = 3(ax-b/x)^3. Given that f(3/2) = 3 and f'(3/2) = 30, find a and b.
Click here to see answer by CPhill(1959)

Question 1190722: According to Census.gov, in 2019 there were approximately 2.7 million people working at janitors and building cleaners. Approximately 11% of these were classified as having at least one disability. The most common disability types for workers were ambulatory, hearing, cognitive, and vision.
Let f(d)=d⋅0.30 where d represents the total number of janitors and building cleaners working with a disability. Let d=g(j)=j⋅0.11 where j represents the total number of janitors and building cleaners. Find the function f(g(j)). If f(d) gives the number of janitors and building workers who have an ambulatory disability, and g(j) represents the number of janitors and building cleaners with a disability, what does f(g(j)) represent? Find f(g(j)) for 2019.
Click here to see answer by CPhill(1959)

Question 1190622: According to Census.gov, in 2019 there were approximately 2.7 million people working at janitors and building cleaners. Approximately 11% of these were classified as having at least one disability. The most common disability types for workers were ambulatory, hearing, cognitive, and vision.
Let f(d)=d⋅0.30 where d represents the total number of janitors and building cleaners working with a disability. Let d=g(j)=j⋅0.11 where j represents the total number of janitors and building cleaners. Find the function f(g(j)). If f(d) gives the number of janitors and building workers who have an ambulatory disability, and g(j) represents the number of janitors and building cleaners with a disability, what does f(g(j)) represent? Find f(g(j)) for 2019.
Click here to see answer by CPhill(1959)

Question 1190596: Determine a, h and k, of the translated function `g(x)`based from the description, then write the equation of the quadratic function in vertex form.
1.) The graph of f(x)=2x^2 is reflected across the x-axis, shifted 6 units to the right and 1 unit upward.
Identify a, h and k: (give the values only no need to explain)
Equation for #1:
2.) The graph of f(x)=x^2 is shifted half unit down and half unit to the right.
Identify a, h and k:
equation for #2:
3.) The parent function ff(x)=2x^2 is reflected across the x-axis and translated 9 units right and 5 units up.
Identify a, h and k:
equation for #3:
Click here to see answer by CPhill(1959)

Question 1190571: Given that
f(x) = (2x-5)/(x+2), g(y)= y^2-3 and p(r)= 10/|r|-1
Find in exact form (a)f(0) (b)p(-4)
Click here to see answer by CPhill(1959)

Question 1190482: Create and describe a function related to kitchen supplies. Give a detailed explanation of the domain (input) and range (output). Then, respond to the following.
What values make up the domain? What values make up the range?
Does it make sense for the function to have a root? What would the root describe?
What would the x- and y-intercepts represent for your function?
Does it make sense for your function to have an inverse? Explain.
Describe a situation where your function becomes an equation that can be solved. Solve.
Click here to see answer by CPhill(1959)

Question 1189813: My teacher asked me to do a roller coaster with polynomial function, he gave me the following requirements:
- your coaster ride must have at least 3 relative maxima and/or minima
- the ride length must be at least 2 minutes (120 seconds)
- the coaster ride starts at 250 feet
- the ride dives below the ground into a tunnel at least once
1. List all roots or x-intercepts of your polynomial; be sure to include at least one of each of the following on your
design: one double root (multiplicity of two) and at least 2 real roots.
Remember: The x-intercepts you select will be somewhat random. You will have to play around with the intercepts
you choose to get a picture of the graph that you like and is accurate. You should use time in seconds as your
independent variable. Your ride has to be at least 2 minutes (120 seconds long) so keep that in mind when you are
selecting x-intercepts to use.
2. Create an equation using your x-intercepts (from question #1) and the y-intercept. Explain how you create your equation.
Avoid using digits 1 and 2 as x-intercepts
Click here to see answer by CPhill(1959)

Question 1209603: What is the range of the function g(x) = (6x + 7)(2x - 3)?
Click here to see answer by Edwin McCravy(20054)

Question 1209604: The domain of the function p(x) = x^2 + 8x + 7x^3 is (-infty,infty). What is the range?
Click here to see answer by ikleyn(52750)

Question 1209602: What is the domain of the function g(x) = (6x + 7)(2x - 3)?
Click here to see answer by ikleyn(52750)

Question 1209601: What is the range of the function f(x) = sqrt(5 - 8x + x^2)?
Click here to see answer by ikleyn(52750)

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