81.5k views
3 votes
Let f(x) = Võ - 6 and g(x) = x2 + 5.(fog)(x) =.(gof)(x) =

Let f(x) = Võ - 6 and g(x) = x2 + 5.(fog)(x) =.(gof)(x) =-example-1
User Fons
by
9.2k points

1 Answer

2 votes

Recall the following:


\begin{gathered} (f\circ g)(x)=f(g(x)), \\ (g\circ f)(x)=g(f(x)). \end{gathered}

Therefore:


\begin{gathered} (f\circ g)(x)=f(x^2+5)=\sqrt[]{(x^2+5)}-6, \\ (g\circ f)(x)=g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5. \end{gathered}

Answer:

Simplifying the above equations we get:


\begin{gathered} (f\circ g)(x)=\sqrt[]{x^2+5}-6, \\ (g\circ f)(x)=(\sqrt[]{x}-6)^2+5=x-12\sqrt[]{x}+36+5=x-12\sqrt[]{x}+41, \\ (g\circ f)(x)=x-12\sqrt[]{x}+41. \end{gathered}

User Jose Armesto
by
8.2k points

Related questions

asked Jun 27, 2024 37.1k views
Msvcyc asked Jun 27, 2024
by Msvcyc
8.5k points
1 answer
5 votes
37.1k views
1 answer
3 votes
46.9k views
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