Sender: "Leanne Hickey"

Subject: inverses of functions
heres the question....

Let f(x) = 2x^{2} -3x + 2. Find f^{-1}(4) given the fact that f(2) = 4. So the question is finding the inverse of 4, he said it's easier than it looks.

thanks alot

Hi Leanne,

Functions behave like the square root button on a calculator. You give it a number and it gives you an answer. If you give the square root function the number 16 it gives you the answer 4. For your function f(x) = 2x^{2} -3x + 2 if you give it the input number 2 it gives you the answer 4 and if you give it the input number 3 it gives you the answer 11.

Inverse functions work like Jeopardy, you give it the answer and it tells you the input number. You tell f^{-1} that the answer was 4 and it replies that the input number was 2. You tell it that the answer was 11 and it tells you that the input number was 3. That is f^{-1}(4) = 2 and f^{-1}(11) = 3.

You do have to take some care with inverses of functions as two different input numbers might give the same answer. If you check you will see that f(-1/2) is also 4 so f^{-1}(4) might be -1/2.