Question

Find (g∘w)(x)and (w∘g)(x)for g(x)=7x−4 and w(x)=x2−7x+3(g∘w)(x)=(w∘g)(x)=

Answer 1

In order to calculate the composite function (gow)(x), that is, g(w(x)), we need to use w(x) as the input (value of x) in the function g(x).

So we have:

`\begin{gathered} g(x)=7x-4 \\ g(w(x))=7w(x)-4 \\ g(w(x))=7(x^2-7x+3)-4 \\ g(w(x))=7x^2-49x+21-4 \\ g(w(x))=7x^2-49x+17 \end{gathered}`

Now, calculating (wog)(x), we have:

`\begin{gathered} w(x)=x^2-7x+3 \\ w(g(x))=g(x)^2-7g(x)+3 \\ w(g(x))=(7x-4)^2-7\cdot(7x-4)+3 \\ w(g(x))=49x^2-56x+16-49x+28+3 \\ w(g(x))=49x^2-105x+47 \end{gathered}`