Mathematics

Problem

Consider the function

f(x)=\sqrt{x-2}+1

, defined for

x\ge 2

. (i) Find

f^{-1}(x)

. (ii) Solve

f(x)=f^{-1}(x)

and hence state the coordinates of the point(s) where the graphs of

f

and

f^{-1}

intersect. a. (i) b. (ii)

Intuitive explanation

To find an inverse function, swap the roles of input and output, then solve for the new output—this "undoes" what the original function does. Once you have $f^{-1}(x)$ , intersections of $f$ and $f^{-1}$ occur where both functions give the same $y$ -value for the same $x$ -value, which often means looking for points that lie on the line $y=x$ (where a function and its inverse always meet).

Intuitive explanation

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