Question

Consider the function.f(x) = x2 − 1, x ≥ 1

Answer 1

t Given

`f(x)=√(x^2-1)`

Find

inverse of f(x)

domain and range of function and its inverse

Step-by-step explanation

Let y = f(x)

`y=√(x^2-1)`

replace all x with y and y with x

`x=√(y^2-1)`

now solve for y

`\begin{gathered} √(y^2-1)=x \\ y^2-1=x^2 \\ y^2=x^2+1 \\ y=\pm√(x^2+1) \end{gathered}`

so, the inverse is

`\pm√(x^2+1)`

domain of f(x) is

`x\epsilon R:x\leq-1\text{ or x}\ge1`

range of f(x) is

`y\epsilon R:y\ge0`

domain of inverse is

`R`

range of inverse function is

`y\epsilon R:y\ge1`