Question

Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain

Answer 1

ANSWER

$f(g(x)) = {x}^{2} + 2x$

EXPLANATION

The given functions are:

$f(x) = {x}^{2} - 4$

and

$g(x) = x + 2$

We want to find

$f(g(x)) = f(x + 2)$

We substitute x+2 wherever we see x in f(x).This implies that;

$f(g(x)) = (x + 2)^{2} - 4$

We can rewrite the perfect square term as

$f(g(x)) = (x + 2)(x + 2)- 4$

We expand to get:

$f(g(x)) = {x}^{2} + 2x + 4- 4$

This simplifies to

$f(g(x)) = {x}^{2} + 2x$

This is a polynomial function. The domain of this function is the values of x for which the function is defined. Since polynomials are defined for all real values, the domain is all real numbers.