Question

Given that g(x) = x2 – 3x - 6, find (gºg)(-2)(gºg)(-2)=

Answer 1

The given function is

`\begin{gathered} x^2-3x-6 \\ \text{gog(x)}=(x^2-3x-6)^2-3(x^2-3x-6)-6 \\ \text{Here to get gog(x), the fuunction g(x) is writtenin place of x variable in g(x) function} \end{gathered}`

Substitute x=-2 in the function gog(x)

`\begin{gathered} \text{gog(-2)}=((-2)^2-3\ast-2-6)^2-3((-2)^2-3\ast-2-6)-6 \\ =(4+6-6)^2-3(4+6-6)-6 \\ =4^2-3\ast4-6 \\ =16-12-6 \\ =-2 \end{gathered}`

Therefore, the value of gog(-2) is -2