Given two functions f(x) and g(x), its composition will be:
[tex](g\circ f)=g(f(x))[/tex]
It is read g compound f or simply said to g we are going to fill it with f. So, you have
[tex]\begin{gathered} (g\circ f)=g(f(x)) \\ (g\circ f)=(2x-3)^3+(2x-3) \end{gathered}[/tex]
To expand the binomial, apply the binomial formula to the cube, that is:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]
So, you have
[tex]\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}[/tex]
Finally, operate similar terms
[tex](g\circ f)=8x^3-36x^2+56x-30[/tex]
