Question

Giving brainliest :)

Answer 1

Answer:

$f^{-1}(x)=x^2+1$

Step-by-step explanation:

The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y

Original Equation:

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

write f(x) as y (since that's what it represents)

$y=\sqrt{x-1}$

Swap x and y

$x=\sqrt{y-1}$

Square both sides

$x^2=y-1$

Add 1 to both sides

$x^2+1=y$

So this gives you the equation:

$f^{-1}(x)=x^2+1$