Question

Which equation is the inverse of y = 2x2 – 8? y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot y = StartFraction plus-or-minus StartRoot x + 8 EndRoot Over 2 EndFraction y = plus-or-minus StartRoot StartFraction x Over 2 EndFraction + 8 EndRoot y = StartFraction plus-or-minus StartRoot x EndRoot Over 2 EndFraction + 4

Answer 1

Answer:

y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot

$y=\pm\sqrt{\frac{x+8}{2}}$

Step-by-step explanation:

Given:

The equation to find inverse is given as:

$y=2x^2-8$

In order to find the inverse, we apply the following steps.

Step 1: Switch 'y' with 'x' and 'x' with 'y'. Thi gives,

$x=2y^2-8$

Step 2: Now, again rewrite the above equation in terms of 'y'.

Adding 8 on both sides, we get:

$x+8=2y^2-8+8$

$x+8=2y^2$

Now, rewriting 'y' terms on the left side of the equation, we get

$2y^2=x+8$

Dividing both sides by 2, we get:

$\frac{2y^2}{2}=\frac{x+8}{2}\\\\y^2=\frac{x+8}{2}$

Taking square root on both sides, we get:

$\sqrt{y^2}=\pm\sqrt{\frac{x+8}{2}}\\\\y=\pm\sqrt{\frac{x+8}{2}}$

Thus, the inverse of the given equation is $y=\pm\sqrt{\frac{x+8}{2}}$.

So, the first option is correct.

Answer 2

Answer: A

Step-by-step explanation: No cap