Question

2. Consider the function .f(x)2/5 x- 4

a.) Find the inverse of f(x) and name it g(x). Show and explain your work.
b.) Use composition to show that f(x) and g(x) are inverses of each other.
c.) Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.

Answer 1

First change f(x) to y, then switch x with y and solve for y. So, x = 2/5 y - 4. Then, x + 4 = 2/5 y, then 5/2 x + 10 = y. g(x) = 5/2 x + 10. Substitute g(x) into f(x) to get 2/5 x - 4 = 5/2 x + 10 and solve (let you figure this out). Finally, just graph the two as lines.