Question

If f(x)=x+4 and g(x)=2x^2-x-1, evaluate the composition (gof)(2)

Answer 1

Given

`\begin{gathered} f(x)=x+4 \\ \text{and} \\ g(x)=2x^2-x-1 \end{gathered}`

Evaluate the composition (gof)(2)​​

Solution

`\begin{gathered} f(x)=x+4 \\ g(x)=2x^2\text{ -x-1} \\ (\text{gof)}(2)=g(f(2) \\ f(x)=x+4 \\ f(2)=2+4 \\ f(2)=6 \end{gathered}`
`\begin{gathered} (\text{gof)}(2)=g(f(2))=g(6) \\ =2(6)^2-6-1_{} \\ =2(36)-6-1 \\ =72-6-1 \\ =72-7 \\ =65 \end{gathered}`