Question

The function f is one-to-one. Find its inverse.

f(x) = 6x^2 + 5, x ≥ 0

Answer 1

First replace f(x) with y\[y = 6x^2 + 5\] switch the x's and y's\[x = 6y^2 + 5\] solve for y \[y = \pm \sqrt{\frac{x-5}{6}}\]

Answer 2

oops then replace y with f^-1(x)\[f^{-1}(x) = \pm \sqrt{\frac{x-5}{6}}\]

Answer 3

but don't forget that
\[x>0\] so
\[f(x)>6\] and therefore only take the positive root. otherwise you do not have a function

Answer 4

excuse me i meant
\[x>0\] so
\[f(x)>5\]