Question

If y = 4x2 – 16, what is its inverse?inverse of y is equal to negative square root of the quantity x over 4 end quantity plus 16 such that x ³ 0inverse of y is equal to negative square root of the quantity x over 4 end quantity plus 16 such that x ² 0inverse of y is equal to negative square root of the quantity x plus 16 over 4 end quantity such that x ² –16inverse of y is equal to negative square root of the quantity x plus 16 over 4 end quantity such that x ³ –16

Answer 1

$\begin{gathered} \text{Given} \\ y=4x^2-16 \end{gathered}$

Change y to x, and x to y

$y=4x^2-16\Longrightarrow x=4y^2-16$

Now that we have swapped x and y, solve for y.

$\begin{gathered} x=4y^2-16 \\ -4y^2=-x-16 \\ \frac{-4y^2}{-4}=\frac{-x-16}{-4} \\ \frac{\cancel{-4}y^2}{\cancel{-4}}=\frac{-x}{-4}+\frac{-16}{-4},\text{ division by two negatives results into positive} \\ y^2=\frac{x+16}{4} \\ \sqrt[]{y^2}=\sqrt[]{\frac{x+16}{4}} \\ y=\sqrt[]{\frac{x+16}{4}} \\ \\ \text{Therefore, the inverse of the given function is} \\ y^{-1}=\pm\sqrt[]{\frac{x+16}{4}} \end{gathered}$