If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given [tex]f(x)=x+7[/tex], the inverse is such that
[tex]f\left(f^{-1}(x)\right) = f^{-1}(x)+7 = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]f^{-1}(x)+7=x \implies \boxed{f^{-1}(x)=x-7}[/tex]
