Question

If f(x) = x2 -1, what is the equation for f–1(x)?

Answer 1

Answer:

$f^{-1}=+-\sqrt{x+1}$

Step-by-step explanation:

f(x) = x^2 -1

We need to find f^-1(x)

WE find inverse of f(x)

Replace f(x) with y

$y= x^2 -1$

Replace x  with y  and y with x

$x= y^2 -1$

Solve for y

add 1 on both sides , $x+1= y^2$

To remove square , take square root on both sides

$\sqrt{x+1} =\sqrt{y^2}$

$\sqrt{x+1} =y$

$y=+-\sqrt{x+1}$

Replace y with f^-1

$f^{-1}=+-\sqrt{x+1}$

Answer 2

Answer:

Inverse function is

$f^{-1}(x)=\pm \sqrt{x+1}$

Step-by-step explanation:

Given that $f(x)=x^2-1$

Now using that equation of f(x), we need to find equation of the inverse function

$f(x)=x^2-1$

$f^{-1}(x)$

Step 1: Replace $f^{-1}(x)$ with y

$y=x^2-1$

Step 2: Switchx and  y

$x=y^2-1$

Step 3: Solve for y

$x=y^2-1$

$x+1=y^2-1+1$

$x+1=y^2$

$y^2=x+1$

take square root of both sides

$y=\pm \sqrt{x+1}$

Hence inverse function is

$f^{-1}(x)=\pm \sqrt{x+1}$