#### Question

# Algebra Help Please!? multi choice(:?

1. Use the functions to answer the question.

f(x) = x2 + 3; g(x) = 6x

Which is equal to (f ? g)(x)?

6x2 + 3

6x3 + 18x

36x2 + 3

36x2 + 18

2. Use the functions to answer the question.

f(x) = 4x – 5; g(x) = x + 3

Which is equal to (g ? f)(x)?

4x – 2

4x + 7

4x + 12

5x – 2

3. Use the functions to answer the question.

f(x) = 2x + 1; g(x) = x2

Which is the value of (f ? g)(–5)?

-49

-19

51

11

5. Use the function to answer the question.

f(x) = 10 – x

What is the value of (f ? f)(3)?

1

3

7

8

#### Answers

1. f(x) = x2 + 3; g(x) = 6x

(f ? g)(x) = f(6x) = (6x)^2 + 3 (quite simply, replace x with 6x in the definition of f(x) )

= 36x^2 + 3

(choice number 3)

2. f(x) = 4x – 5; g(x) = x + 3

g(f(x)) = g(4x - 5) = (4x - 5) + 3 (again, replace x with 4x - 5 in the definition of g(x) )

= 4x - 2

(choice 1)

3. f(x) = 2x + 1; g(x) = x2

f(g(-5)) = f( (-5)^2) = f(25) (first simplify the value of g(x) at x = -5)

= 2*25 + 1 (put in x = 25 in f(x) )

= 51

(choice 3)

4. f(x) = 10 – x

f(f(3)) = f(10-3) = f(7) = 10 - 7 = 3

(choice 2)