Chapter 10 - Radical Functions and Equations - 10.4 - Inverse of a Function - Exercises - Page 572: 14

$x=\pm \sqrt {2y+14}$ When output $y=2$, input $x=\pm3\sqrt 2$

$y=\frac{1}{2}x^{2}-7$ Add $7$ to both sides of the equation to get $y+7=\frac{1}{2}x^{2}$ Multiplying by $2$ on both the sides, we obtain $2y+14=x^{2}$ Taking square root on both the sides, we have $x=\pm \sqrt {2y+14}$ When output $y=2$, Input $x=\pm\sqrt {2(2)+14}=\pm3\sqrt 2$