Question

Given that f(x) = 4x - 7 and g(x) = 4x, find a simplified expression for f(f(x)).

Answer 1

Given:

$f(x)=4x-7$

$g(x)=4x$

To find:

The expression for f(f(x)).

Solution:

We need to find f(f(x)).

$f(f(x))=f(4x-7)$                             $[\because f(x)=4x-7]$

$f(f(x))=4(4x-7)-7$                             $[\because f(x)=4x-7]$

Using distributive property, we get

$f(f(x))=4(4x)+4(-7)-7$

$f(f(x))=16x-28-7$

$f(f(x))=16x-35$

Therefore, the expression for f(f(x)) is $f(f(x))=16x-35$.