Question

I try solve and I no get correct answer! Please help I don’t know

Answer 1

gof means that we must first evalute f at x and next evalute the result in g.

In our case,

`\text{gof(x)}=g(f(x))`

By taking into account that f(x)=3x-1 and g(x)=4x^2+9, we have

`\begin{gathered} (\text{gof)(x)}=g(f(x)=g(3x-1)=4(3x-1)^2+9 \\ \end{gathered}`

In summary,

`(\text{gof)(x)}=4(3x-1)^2+9`

Now, we must substitute x=-2 in this lat equation, It yields

`(\text{gof)(-}2)=4(3(-2)-1)^2+9`

hence, we obtain,

`\begin{gathered} (\text{gof)(-}2)=4(-6-1)^2+9 \\ (\text{gof)(-}2)=4(-7)^2+9 \\ (\text{gof)(-}2)=4\cdot49+9 \\ (\text{gof)(-}2)=196+9 \\ (\text{gof)(-}2)=205 \end{gathered}`

Hence, the answer is 205