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

1-107.

Sandra is playing around with inverses and thinks she has discovered something interesting. She thinks that if f(x) = g–1(x), then the areas of the regions shaded below are equal. Use f(x) = $\frac { 1 } { 3 }$x + 1 with a = 3 and b = 5 to verify Sandra’s conjecture. Homework Help ✎

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

$\text{The area of }f(x)=\frac{1}{2}(b-a)\left [ f(b)+f(a) \right ]$

$\text{The area of }g(x)=\frac{1}{2}(b-a)\left [ f^{-1}(a)+f^{-1}(b) \right ]$

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