Question

if f(x) = 6x^2 -6x -36, find f^-1(x).

Answer 1

i try to take the quadratic and im getting a wrong answer

Answer 2

\[y=6x^{2}-6x-36\Longrightarrow y+36=6(x^{2}-x)\Longrightarrow y+36=6(x^{2}-x+.25)-6(.25)\]
\[y+36 = 6(x-1/2)^{2}-3/2\]
Solving for x gives us:\[x=1/2 +\sqrt(y+36+3/2)/6\]
that would be the inverse, but you need to restrict the domain

Answer 3

this one would have to be split into two separate equations. one from -infinity to 0,
the other from 0 to infinity