Given the functions f (x) = 2x + 5 and g (x) = x2 + 8, which of the following functions represents f (g (x) ] correctly?

1. f[g (x) ] = 4x2 + 20x + 32

2. f (g (x) ] = 4x2 + 20x + 25

3. f[g (x)) = 2x2 + 16

4. f (g (x)) = 2x2 + 21

the answer is D

Choice 4.

Step-by-step explanation:

f (g (x))

Replace g (x) with x^2+8 since g (x) = x^2+8.

f (g (x))

f (x^2+8)

Replace old input, x, in f with new input, (x^2+8).

f (g (x))

f (x^2+8)

2 (x^2+8) + 5

Distribute:

f (g (x))

f (x^2+8)

2 (x^2+8) + 5

2x^2+16+5

Combine like terms:

f (g (x))

f (x^2+8)

2 (x^2+8) + 5

2x^2+16+5

2x^2+21