Answer
$f^{-1} (x)=y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$
Work Step by Step
Let $x$ be exhaust temperature and $y$ be the percent load.
We have $y=0.03x^2+245.50; 0 \lt x \lt 100$
To compute the inverse, we will have to interchange $x$ and $y$.
$x=0.03y^2+245.50; 245.50 \lt x \lt 545.50$
Re-write as: $ x-245.50=0.03; 245.50 \lt x \lt 545.50$
or, $y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$
Replace $y$ with $f^{-1} (x)$.
$f^{-1} (x)=y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$
