Question

3. Find f[h(a+4)], given the functions below. *

Given f(x) = 5x, g(x) = -2x + 1, and h(x) = x2 + 6x + 8, find each value.
O A 2a^2 +15a +120
O B 5a^2 +30a +240
O C 5a^2 +70a +240
O D-5a^2 +50a +360

Answer 1

C 5a^2 +70a +240

Explanation:

We have given these following functions:

`f(x) = 5x, g(x) = -2x + 1, h(x) = x^2 + 6x + 8`

h(a+4)

This function is:

`h(a+4) = (a+4)^2 + 6(a + 4) + 8`

`h(a+4) = a^2 + 8a + 16 + 6a + 24 + 8`

`h(a+4) = a^2 + 14a + 48`

f[h(a+4)]

`f(x) = 5x`

Thus

`f(h(a+4)) = f(a^2+14a+48) = 5(a^2 + 14a + 48) = 5a^2 + 70a + 240`

The correct answer is given by option C.