13 Questions. 1-11 have provided options, 12 and 13 are manual answers.


1. Perform the required operations on the following functions.

Given: f(x) = 3 - x; g(x) = -2x

Find g[f(x)].

Options:

A. -x - 6

B. 2x - 6

C. 2x + 3


2. Perform the required operations on the following functions.

Given: f(x) = 3 - x; g(x) = -2x

Find f[g(2)].

Options:

A. -1

B. 25

C. 7


3. Given: f(x) = 3 - x; g(x) = -2x

Find g[f(-1)].

Options:

A. -22

B. 8

C. -8


4. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Find F[G(x)] - F(x).

Options:

A. 4x + 4

B. 4x

C. 4x + 2


5. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Find G[H(1)].

Options:

A. 5

B. 35

C. 8


6. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x&2

Find F{G[H(2)]}.

Options:

A. 121

B. 27

C. 71


7. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Find H(x + a) - H(x)

Options:

A. a^2

B. a^2 + 2ax

C. 2a


8. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2

Find [H(x + a) - H(x)] / a

Options:

A. 2x + a

B. a

C. a^2 + 2x


9. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Find F(x) + G(x) + H(x).

Options:

A. 5x^3 + 1

B. x^2 + 5x + 3

C. x^2 + 5x + 1


10. If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).

Options:

A. 0

B. 7

C. 17


11. If G(x) = 5x- 2, find G^-1 (x).

Options:

A. (x + 2)/5

B. (x/5) + 2

C. -5x + 2


12. What is the inverse of f(x) ? Show all work for full credit.

f(x) = 2 / [x - 6]


13. Use composition of functions to determine whether f(x) and g(x) are inverses of each other. Show all work for full credit.

f(x) = 4/5 x + 1

g(x) = [5x - 5] / 4