Question

Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below:

f(x) = 6x + 12

g(x) = x − 8

−96
0
24
48

Answer 1

Option 2nd is correct.

`f[g(6)]` =0.

Explanation:

Given the function:

`f(x) = 6x+12`

`g(x) = x-8`

Solve:
`f[g(6)]`

First calculate:

f[g(x)]

Substitute the function g(x)

`f[x-8]`

Replace x with x-8 in the function f(x) we get;

`f(x-8) = 6(x-8)+12`

The distributive property says that:

`a\cdot (b+c) = a\cdot b+ a\cdot c`

Using distributive property:

`f(x-8) = 6x-48+12 = 6x-36`

⇒
`f[g(x)] = 6x-36`

Put x = 6 we get;

`f[g(6)] = 6(6)-36 = 36-36 =0`

Therefore, the value of
`f[g(6)]` is 0.

Answer 2

f[g(6)] = f[6 - 8] = f[-2] = 6(-2) + 12 = -12 + 12 = 0

f[g(6)] = 0

The answer is B) 0.