### Home > CALC > Chapter 1 > Lesson 1.3.1 > Problem1-107

1-107.

Sandra was playing around with inverses and thinks she has discovered something interesting. She thinks that if $f(x) = g^{-1} (x)$, then the area of the regions shaded at right are equal. Use $f ( x ) = \frac { 1 } { 3 } x + 1$ with $a = 3$ and $b = 5$ to verify Sandra's conjecture.

If $f(x)=\frac{1}{3}x+1$ then $f^{-1}(x)=3(x-1)$

Substitute in the values for $a$ and $b$. Are the values equal?