164k views
3 votes
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

For the real-valued functions f (x)=x² +4 and g(x)=x-5, find the composition f g and-example-1

1 Answer

3 votes

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)

User Kenny Basuki
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories