Question

How do you find the inverse of `10=y-2x^2`?

Answer 1

There are two inverse functions, both of which can be found by solving the equation `10=y-2x^2\leftrightarrow y=f(x)=2x^{2}+10` for `x` in terms of `y`: `10=y-2x^2 =>2x^2=y-10 => x=\pm\sqrt{y/2-5}`.

The function `g(x)=\sqrt{y/2-5}` is an inverse function of `f(x)=2x^{2}+10` when the domain of `f` is restricted to `x\geq 0`.

The function `h(x)=-\sqrt{y/2-5}` is an inverse function of `f(x)=2x^{2}+10` when the domain of `f` is restricted to `x\leq 0`.