Function Operations

Inverse Functions

100

Find the inverse of {(2,-2) (4, 0) (6, -3) (-7, 2)}

{(-2, 2), (0, 4), (-3, 6) (2, -7)}

200

State if the given functions are inverses, show all work. f(n) = 2(n-2)³ g(n) = 2 + 1/2(4n)^1/3

Hint -exponent ^1/3 is the same as cube root

Yes

300

Find the inverse of the given function, h(x)=(x)^1/3 -3

(x+3)³

400

State if the given functions are inverses, show all work. g(x) = 4 - (3/2)x       f(x) = (1/2)x + (3/2)

No, because fog(x) and gof(x) do not equal x.

500

Find the inverse of g(x) = ¹/_(x-1)

What is 1+ (¹/_x)

Addition

100

Let f(x)=4x-1 and g(x)=2x²+3. Then f(x)+g(x) equals what?

What is 2x² + 4x + 2

200

Let f(x)=-3x+2 and g(x)=5-x. Then f(x)+g(x) equals what?

What is -4x + 7

300

Let f(x)=3x+5 and g(x)=x². Then (f+g)(2) equals what?

What is 15

400

Let f(x)=3x+5 and g(x)=x^2. Then f(x)+g(x) equals what?

What is x² + 3x + 5

500

Let f(x)=x²-5 and g(x)=3x+2. Then f(3)+g(3) equals what?

What is 15

Subtraction

100

Let f(x)=4x-1 and g(x)=2x²+3. Then f(x)-g(x) equals what?

What is -2x² + 4x - 4

200

Let f(x)=4x-1 and g(x)=2x²+3. Then (g-f)(5) equals what?

What is 34

300

Let f(x)=-3x+2 and g(x)=-2x²+9. Then f(x)-g(x) equals what?

What is 2x² - 3x - 7

400

Let f(x)=3x+5 and g(x)=x². Then (f - g)(7) equals what?

What is -23

500

Let f(x)=2x²+x-3 and g(x)=x-1. Then (f-g)(5) equals what?

What is 48

Multiplication and Division

100

Let f(x)=4x-1 and g(x)=2x²+3. Then f(x)*g(x) equals what?

What is 8x³ - 2x² + 12x - 3

200

Let f(x)=-3x² -x and g(x)=-2x -4. Then (f * g)(-1)

4

300

Let f(x)=2x and g(x)=x-1. Then f(6)/g(6) equals what?

12/5

400

Let f(x)=x²-5 and g(x)=3x+2. Then f(-5)/g(-5) equals what?

What is -20/13

500

What is 5 * 3?

15

Composite Functions and Word problems

100

Let f(x)=3x²+2 and g(x)=2x. Then (f o g)(x) equals what?

What is 12x² + 2

200

Let f(x)=3x²+2 and g(x)=2x. Then (g o f)(x) equals what?

What is 6x² + 4

300

Let f(x)=3x and g(x)=2x+4. Then (f o g)(1) equals what?

What is 18

400

Classes at Maricopa Community Colleges are $86 per credit hour. All students registering to take classes were also required to pay a $15 registration fee.Write the equation, then find the inverse. 

f(x) = 15+86x

f^-1(x) = ^(x-15)/₈₆

500

At your job, you are paid $100 a day plus $5 for each dog walked. The equation is f(x) = 100 + 5x. What is the inverse of this function? If you made $175, how many dogs did you walk?

f^-1(x) = x-100/5

15 dogs