Question

Please help, how do I get the inverse of this function?

Answer 1

solve for x

Answer 2

then switch x and y

Answer 3

i hit a roadblock while trying to solve for x

Answer 4

To get an inverse, a quick trick would be to replace the x and y, and solve for y.
\[
y=\sqrt{x^2+9x}
\]So, we do:
\[
x=\sqrt{y^2+9y}\implies\\
x^2=y^2+9y\implies\\
x^2+\frac{81}{4}=y^2+9y+\frac{81}{4}\implies\\
x^2+\frac{81}{4}=\left(y+\frac{9}{2}\right)^2\implies\\
\pm\sqrt{x^2+\frac{81}{4}}=y+\frac{9}{2}\implies\\
y=\frac{9}{2}\pm\sqrt{x^2+\frac{81}{4}}
\]And we are done.

Answer 5

Wait, sorry, it is \[y=-\frac{9}{2}\pm\sqrt{x^2+\frac{81}{4}}\]

Answer 6

Thanks so much @LolWolf and @oswalde2000

Answer 7

Sure thing.