Assume that the function f is a one-to-one function. (a) If f(9)=4, find f-1(4) Answer? (b) If f-1(-9)=-4, find f(-4). Answer?

Question

Assume that the function f is a one-to-one function.

(a) If f(9)=4, find f^-1(4)

Answer?

(b) If f^-1(-9)=-4, find f(-4).

Answer?

Thank you

[3.7_1]

Answer 1

f(9)= - 4; f^-1 (- 4) = 9

f^-1(- 9) = - 4; f(- 4) = - 9

Answer 2

Here are a few ways to think about a function and its inverse:

1. If f(x) produces y, then putting y into the inverse of f produces the output x

2. f^-1(f(x)) = x and f(f^-1(x)) = x

For your examples:

(a) f^-1(4) = f^-1(f(9)) = 9

(b) f(-4) = f(f^-1(-9)) = -9