Question

Given the functions f(x) = 10x + 25 and g(x) = x + 8, which function represents f[g(x)] correctly?

A.) f[g(x)] = 10x + 33
B.) f[g(x)] = 10x2 + 33
C.) f[g(x)] = 10x + 105
D.) f[g(x)] = 10x2 + 105

Answer 1

Option C is correct

the function f[g(x)] represents correctly is:
`10x+105`

Explanation:

Given the function:

`f(x) = 10x+25` and
`g(x) = x+8`

then;

`f[g(x)]`

Substitute the function g(x) we have;

⇒
`f[x+8]`

Replace x with x+8 in f(x) we have;

⇒
`f[x+8] = 10(x+8)+25`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

⇒
`f[g(x)] = 10x+80+25 = 10x+105`

Therefore, the function f[g(x)] represents correctly is:
`10x+105`

Answer 2

It's asking for a composition function where you insert the function g(x) into f(x).
f(g(x))=10(x+8)+25
f(g(x))=10x+80+25
f(g(x))=10x+105