Question

Find the domain and range of the inverse relation ofR={(x, y): y≥x² - 2 and y≤2)

Answer 1

We can find the inverse relation by solving the inequalities for x, then we have:

$\begin{gathered} y\ge x^2-2 \\ \Rightarrow y+2\ge x^2 \\ \Rightarrow-\sqrt[]{y+2}\le x\le\sqrt[]{y+2} \end{gathered}$

therefore, the domain and range of the inverse relation of R is:

$R^{\prime}=\mleft\lbrace(x,y\mright)\colon-\sqrt[]{y+2}\le x\le\sqrt[]{y+2}\text{ and y}\leq2\}$