Let f(x) = x2 − 16. Find f−1(x)

Answer 1

I'm going to assume that f(x) = x² - 16 and that you are trying to find the inverse, f^-1(x). I'm also going to assume that we consider x > 0. Without making that final assumption, the result is that there is no inverse function.

Step 1: Temporarily replace "f(x)" with "y" to get: y = x² - 16

Step 2: Switch the places of the "x" and "y" to get: x = y² - 16

Step 3: Solve for "y":

x = y² - 16

x + 16 = y²

y = √(x + 16)

Step 4: Replace "y" with "f^-1(x)" to get: f^-1(x) = √(x + 16)