Question

Need help getting clarification on how to solve this and broke it down so I know how to in the future.

Answer 1

The function composition definition is shown below

`(f\circ g)(x)=f(g(x))`

Then, our case

a)

`\begin{gathered} (f\circ g)(x)=f(g(x))=f(x^2-5)=(x^2-5)^2+5 \\ \Rightarrow(f\circ g)(x)=(x^2-5)^2+5 \end{gathered}`

Simplifying the answer,

`\begin{gathered} \Rightarrow(f\circ g)(x)=x^{4^{}}-10x^2+25+5=x^{4^{}}-10x^2+30 \\ \Rightarrow(f\circ g)(x)=x^{4^{}}-10x^2+30 \end{gathered}`

The answer is x^4-10x^2+30.

Explanation of (x^2-5)^2

`\begin{gathered} (x^2-5)^2=(x^2-5)(x^2-5)=x^2\cdot x^2-5\cdot x^2-x^2\cdot5+(-5)(-5)=x^4-5x^2-5x^2+25 \\ \Rightarrow(x^2-5)^2=x^4-10x^2+25 \end{gathered}`