To get h^-1(x), we have to replace x for h(x) and vice versa in the original function:
[tex]h(x)=x^2+1[/tex][tex]x=(h^{-1}(x))^2+1[/tex]
Solving for h^-1(x):
[tex]\sqrt{x-1}=\sqrt{(h^{-1}(x))^2}[/tex][tex]h^{-1}(x)=\pm\sqrt[]{x-1}[/tex]
Graph:
The red function in the graph represents:
[tex]h(x)=x^2+1[/tex]
The blue function represents:
[tex]h^{-1}(x)=+\sqrt[]{x-1}[/tex]
The green function represents:
[tex]h^{-1}(x)=-\sqrt[]{x-1}[/tex]
The graph of f(x)
