as you already know, to find the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf y=5x^2+11\implies \stackrel{\textit{switcheroo}}{x=5y^2+11}\implies x-11=5y^2\implies \cfrac{x-11}{5}=y^2 \\\\\\ \sqrt{\cfrac{x-11}{5}}=y\impliedby f^{-1}(x)\qquad \{x|~x\ge 11\}[/tex]
why x ⩾ 11? because if say x = 10 for example, for the numerator we'd get (10) - 11 = -1.
that gives us a radicand of -1/5, and recall a square root with a negative radicand, is not a real number root, is an imaginary one.
