Question

) Given that f (x) is a one-to-one function and and f (3) =-4, f (-1) = 6, and f (2) = 3 find f -^1(3).
. Explain in 1 or 2 sentences how you know what the answer is. (10 points)
f (x) f (3) = −4, f (−1) = 6, f (2) = 3
f (3) −1
6
−4
2
-1

Answer 1

f^{-1}(3) = 2.

Since f(2) = 3 and the inverse function swaps inputs and outputs, f^{-1}(3) = 2; the one-to-one property guarantees the inverse exists.