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Tutors Answer Your Questions about Functions (FREE)
Question 45202: Find the maximum or minimum value of the function:
f(x) = 1 + 3x -x^2
= x^2 + 3x + 1
=-(x^2 -3x + 2.25) +1 + 2.25
=-(x^2 -3x + 2.25) + 3.25
x= -b/2a = -3/2(-1) = 3/2 = max 1.5
y = 3.25
Thank you so much!
Click here to see answer by rapaljer(4667)  |
Question 45205: Find the maximum or minimum value of the function
f(x) = -x^2/3 + 2x + 7
x = 2/2(-1/3) = 2/(-2/3)= (2/1)(3/2)= 3 maximum
(-x^2 + 6x + 21 /3) = ((-x^2 + 6x + 9) + 21 + 9)/3)
= (-(x + 3)^2 + 30)/3
= -(x + 3)^2 + 10
y = 10
Thanks so much!
Click here to see answer by rapaljer(4667)  |
Question 45369: It's been 15 years since I've taken algebra, please show me how you got to the answer.
If f(4)=0 and f(6)=6, what could represent f(x)?x can represent anyone number that solves the equation
Click here to see answer by hope(1) |
Question 45520: Use the property of Inverse Functions to show that f and g are inverses of each other:
f(x) = x^3 + 1; g(x) = (x-1)^(1/3)
f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x
g(f(x)) = g(x^3 + 1) = (x^3 + 1)^3 + 1 = x + 1 -1 = x
f and g are inverses of each other.
Thank you very much!
Click here to see answer by stanbon(57407) |
Question 45518: Use the Property of Inverse Functions to show that f and g are inverses of each other:
f(x) = 2x, g(x) = x/2
f(g(x)) = f(x/2) = 2(x/2) = x
g(f(x)) = g(2x) = 2(x/2) = x
f and g are inverses of each other, correct?
Thank you very much!
Click here to see answer by stanbon(57407) |
Question 45583: A company produces a product for which the variable cost is $10.20 per unit and the fixed cost is $13000.The product sells for $ 19.99.Let x be the number of unitsproduced and sold.
a)Write the total cost of C as a function of the number of units produced.
b)Write the revenue R as a function of the number of units sold
c)Write the profit P as a function of the number of units sold.
Click here to see answer by stanbon(57407) |
Question 45654: I told my grandson I would help with his homework and I don't have the heart to tell him I don't know it Could you answer these questions for me:
Why is function notation important? and what's the reasons for function notation? I have not the slightest idea, can you help me on this one?
Bless you heart.....Bessie
Click here to see answer by stanbon(57407) |
Question 45790: From a square piece of cardboard with width x inches, a square of width x-3 inches is removed from the center. Write the area of the remaining piece as a function of x.
I am at a loss on how to start solving this one.
Click here to see answer by checkley71(8403) |
Question 45850: the following two lines represent a function: line (1) has points a(-3,1) b(-1,4) line (2) has points c(1,3) and d(4,1). Give the domain of the function.
i know from my reading it says the Domain is the highest values that make the function work. but i am not sure what that means given the data above.
Click here to see answer by tutorcecilia(2152)  |
Question 45851: values of two functions (f) and (g) are listed below find the composite (f little circle g)(6).
values for (f) [x=4 f(x)=7 ] for [x=5 f(x)=6] [for x=6 f(x)=5] [x=7 f(x)=4]
values for (g) [x=4 g(x)=6 ] for [x=5 g(x)=7] [for x=6 g(x)=4] [x=7 g(x)=5]
i know from my reading that the composite = f(g(x))
so does that mean i just go to the list and find what g(6)= which is 4.
to find my answer. is it that simple.
Click here to see answer by stanbon(57407) |
Question 45881: How do I even apprehend this? Can you explain each step for me please.
Thanks.
If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function P(x)=2.25x-7000
(a) What is her profit if she sells 2000 units?
(b) What is her profit if she sells 5000 units?
(c) What is the break-even point for sales?
Click here to see answer by Earlsdon(6287) |
Question 46288: Question is: Give the domain of square root of x + 1 over x in interval notation. My first answer was (-infinity, 0) U (0, infinity). I got the second part right but I did not get the first part of the answer right. I know that the reciprocal function f(x) = 1/x contains the domains of (-infinity, 0)U (0, infinity) but apparently this does not help me. Can anyone help?
Click here to see answer by AnlytcPhil(1278)  |
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