Question

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

Answer 1

`\bf \begin{cases} f(x)=&10x+25\\ g(x)=&x+8 \end{cases}~\hspace{5em} \begin{array}{llll} f(~~g(x)~~)=&10[g(x)]+25\\\\ f(~~g(x)~~)=&10[x+8]+25\\\\ f(~~g(x)~~)=&10x+80+25\\\\ f(~~g(x)~~)=&10x+105 \end{array}`

Answer 2

f(g(x)) = 10x + 105

Explanation:

Start with f(x) = 10x + 25. Replace this x with (x + 8), which is g(x):

f(g(x)) = 10(x + 8) + 25, or

= 10x + 80 + 25, or 10x + 105

f(g(x)) = 10x + 105