Question

-Exponential and Logarithmic Functions- If h(x)=x²+ 1, state a rule for...

Answer 1

To get h^-1(x), we have to replace x for h(x) and vice versa in the original function:

`h(x)=x^2+1`
`x=(h^(-1)(x))^2+1`

Solving for h^-1(x):

`√(x-1)=\sqrt{(h^(-1)(x))^2}`
`h^(-1)(x)=\pm\sqrt[]{x-1}`

Graph:

The red function in the graph represents:

`h(x)=x^2+1`

The blue function represents:

`h^(-1)(x)=+\sqrt[]{x-1}`

The green function represents:

`h^(-1)(x)=-\sqrt[]{x-1}`

The graph of f(x)