Question

I am trying to simplify a composition of functions.(f o g) (7.5)f(x) = -x + 7f(g) = -4x -2

Answer 1

There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have

`\begin{gathered} (f\circ g)(x)=-(-4x-2)+7 \\ (f\circ g)(x)=4x+2+7 \\ (f\circ g)(x)=4x+9 \end{gathered}`

We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get

`\begin{gathered} (f\circ g)(7.5)=4(7.5)+9 \\ (f\circ g)(7.5)=39 \end{gathered}`

The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got

`\begin{gathered} g(7.5)=-4(7.5)-2 \\ g(7.5)=-32 \\ \Rightarrow\Rightarrow f(-32)=-(-32)+7=39 \end{gathered}`