Answer:
[tex]f^{-1}(x)=x^2+1[/tex]
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:
[tex]f(x)=\sqrt{x-1}\\[/tex]
write f(x) as y (since that's what it represents)
[tex]y=\sqrt{x-1}[/tex]
Swap x and y
[tex]x=\sqrt{y-1}[/tex]
Square both sides
[tex]x^2=y-1[/tex]
Add 1 to both sides
[tex]x^2+1=y[/tex]
So this gives you the equation:
[tex]f^{-1}(x)=x^2+1[/tex]
