Question

Find the inverse y = x^2 - 10x

Answer 1

`\begin{gathered} y=x^2-10x \\ \Rightarrow x^2-10x-y=0 \end{gathered}`
`\Rightarrow(x-5)^2-(-5)^2-y=0`
`\begin{gathered} \Rightarrow(x-5)^2=y+25 \\ \Rightarrow x-5=\pm\sqrt[]{y+25} \end{gathered}`
`\Rightarrow x=\pm\sqrt[]{y+25}+5`

Hence the inverse is given by:

`y=\pm\sqrt[]{x+25}+5`