According to the definition,
[tex](g\circ f)(x)=g(f(x))[/tex]
find the composition
[tex]\begin{gathered} g(f(x))=2(x+5)-1 \\ g(f(x))=2x+10-1 \\ g(f(x))=2x+9 \end{gathered}[/tex]
then, find the inverse of the function,
[tex]\begin{gathered} y=2x+9 \\ switch\text{ }the\text{ }variables \\ x=2y+9 \\ clear\text{ }for\text{ }y \\ x-9=2y \\ y=\frac{x-9}{2} \end{gathered}[/tex]
Answer:
[tex](g\circ f)^{-1}=\frac{x-9}{2}[/tex]
