Question

For the real-valued functions f (x)=x² +4 and g(x)=x-5, find the composition f g and specify its domain using interval notation.0 0.0DOf(x) = 1

Answer 1

Ok, so

We got these two functions:

$\begin{gathered} f(x)=x^2+4 \\ g(x)=x-5 \end{gathered}$

We're going to find the composition (f o g)(x).

This composition is the same that evaluate the function f(x) in g(x).

This is, f (g(x)):

$\begin{gathered} f(x-5) \\ =(x-5)^2+4 \end{gathered}$

Simplifying:

$\begin{gathered} =x^2-10x+25+4 \\ =x^2-10x+29 \end{gathered}$

As these two functions are polynomials, then, the domain of (fog)(x), will be:

$(-\infty,\infty)$