Question

Exercise #99) g(x) = x3 + x f(x) = 2x-3 - 3 Find (gof)(x)

Answer 1

Given two functions f(x) and g(x), its composition will be:

`(g\circ f)=g(f(x))`

It is read g compound f or simply said to g we are going to fill it with f. So, you have

`\begin{gathered} (g\circ f)=g(f(x)) \\ (g\circ f)=(2x-3)^3+(2x-3) \end{gathered}`

To expand the binomial, apply the binomial formula to the cube, that is:

`(a-b)^3=a^3-3a^2b+3ab^2-b^3`

So, you have

`\begin{gathered} (g\circ f)=(2x-3)^3+(2x-3) \\ (g\circ f)=(2x)^3-3(2x)^2(3)+3(2x)(3)^2-(3)^3+(2x-3) \\ (g\circ f)=2^3x^3-3(2^2x^2)(3)+3(2x)9-27+(2x-3) \\ (g\circ f)=8x^3-3(4x^2)(3)+54x-27+(2x-3) \\ (g\circ f)=8x^3-36x^2+54x-27+2x-3 \end{gathered}`

Finally, operate similar terms

`(g\circ f)=8x^3-36x^2+56x-30`