Question

For this question, use the following functions.

f(x) = 2x + 6
g(x) = 4x2 – 9
Find a simplified expression for f(f(x)).
O 2x – 12
0 4x + 12
O 2x + 6
O 4x + 18

Answer 1

4x + 18

Explanation:

This is called a composite function, meaning passing the range of one function as a domain of another function.

For f(f(x)), the inner-function's range is passed as the domain of the outer function.

We can do so by substitution,

The range of f(x) can be written as 2x + 6 for any defined x values,

So we will substitute 2x + 6 as the 'x' of another function which is in this case

f(x) again, so it looks like this 2(2x+6) + 6 which can be simplified into

4x + 18