f(x) = x^2 - 12x, x<=6 (x is less than or equal to 6). Find the inverse of f(x).

Question

f(x) = x² - 12x, x≤6. Find the inverse of f(x).

I was told to use the quadratic equation, but when I do that I get a numerical answer and not an inverse equation.

Answer 1

y = x² - 12x

Interchange x and y

x = y² - 12y => y² - 12y - x = 0

Quadratic formula

y = [12 - sqrt(144 -4x)]/2 = 6 - sqrt(36-x)

I took the minus sign because when I graphed the answer it was obvious that the + sign didn't work.

Remember the graphs of f and its inverse are mirror images about the line y = x.