Question

Given the functions f(x) = 7x + 13 and g(x) = x^2 + 2, which of the following functions represents f[g(x)] correctly?

f[g(x)] = 7x^2 + 27
f[g(x)] = 7x^2 + 15
f[g(x)] = 49x^2 + 182x + 169
f[g(x)] = 49x^2 + 182x + 171

Answer 1

A. f(g(x)) = 7x + 27

We have, f(x) = 7x+13 and g(x) = x+2.

So, the function f(g(x)) is obtained by substituting the function g(x) = x+2 in f(x) = 7x+13,

i.e. f(g(x)) = f(x+2)

i.e. f(g(x)) = 7 × (x+2) + 13

i.e. f(g(x)) = 7x + 14 + 13

i.e. f(g(x)) = 7x + 27

Thus, f(g(x)) = 7x + 27

Answer 2

f(g(x)) = x^2 + 27.

Explanation:

To find f(g(x)) we replace the x in f(x) by g(x) and simplify:

f(g(x)) = 7(x^2 + 2) + 13

= 7x^2 + 14 + 13.

= 7x^2 + 27.