Question

F(x) = square root of x - 5. find f^-1 (x) and it’s domain

Answer 1

Given:

f(x) = root x - 5

Rewrite the function using y,

`y=\sqrt[]{x}-5`

Now, interchange the position of x and y in the function,

`x=\sqrt[]{y}-5`

Isolate the dependent variable

`\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}`

Therefore,

`f^(-1)(x)=(x+5)^2`

And the domain is minus infinity to infinity

`\begin{gathered} f^(-1)(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}`