Question

Find the inverse of the function. y = 2x2 –4

Answer 1

To find inverse functions, switch the two variable and solve for y:

x=2y²-4
x+4=2y²
(x+4)/2=y²
√((x+4)/2)=y

Answer 2

Answer:

The inverse function is $y=\sqrt{\frac{x+4}{2}}$

Step-by-step explanation:

The given function is $y=2x^2-4$.

This function is only invertible on the interval, $x\ge 0$.

To find the inverse on this interval, we interchange $x$ and $y$.

$x=2y^2-4$

We now make $y$ the subject to get,

$x+4=2y^2$

$\Rightarrow \frac{x+4}{2}=y^2$

$\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y$

But the given interval is $x\geq 0$, This implies that, $y\geq 0$.

$y=\sqrt{\frac{x+4}{2}}$