Given the equation:
[tex]x=y^2[/tex]
Solving for y:
[tex]y=\sqrt{x}[/tex]
If we are given the values of y, we use the first equation, otherwise, we use the second equation.
We are required to find the values of y for x ={0, 16, 100} and the values of x for:
[tex]y={}\lbrace\sqrt{5},-2\sqrt{2}\rbrace[/tex]
Calculate the values of y:
x = 0
[tex]y=\sqrt{0}=0[/tex]
x = 16
[tex]y=\sqrt{16}=4[/tex]
x = 100
[tex]y=\sqrt{100}=10[/tex]
Now calculate the values of x.
[tex]x=(\sqrt{5})^2=5[/tex]
Finally:
[tex]\begin{gathered} x=(-2\sqrt{2})^2 \\ \\ x=(-2)^2(\sqrt{2})^2 \\ \\ x=4\cdot2=8 \end{gathered}[/tex]
The table with the completed values is shown below:
