Question 112746
This is an inverse functions problem.  f(x) is read f of x, not f times x and is just a fancy way of saying y.  so really what they are saying is:

{{{y=sqrt(x-1)}}}

To find an inverse, which is what {{{f^(-1)}}} means, you switch the x and y and then solve for the new y:


{{{x=sqrt(y-1)}}}
square both sides:
{{{(x)^2=(sqrt(y-1))^2}}}
so
{{{x^2=y-1}}}
add 1 to both sides
{{{x^2+1=y}}}


This means that the inverse function is:
{{{f^-1(x)=x^2+1}}}