Question

Which equation is the inverse of y = 2x² - 8?

x+8
=t₁ 2
y =
± √√x+8
2
y-√√2+8
y=₁
S
y-√x +4
Y=

Answer 1

The inverse of a function is a function that "undoes" the original function. In other words, if you apply the inverse function to the output of the original function, you get back the input value.

To find the inverse of a function, you can switch the roles of the input and output variables (x and y) and solve for the original input variable.

In this case, the original function is y = 2x^2 - 8. To find the inverse of this function, we can switch the roles of x and y and solve for x:

x = 2y^2 - 8

This is the inverse of the original function. Note that the original function and its inverse are not the same, and they do not have the same graph.

The given options do not include the inverse of the original function, so none of them are correct

Answer 2

The function which reverses into another function is called an inverse function.

From the given data in the question, we have y = 2x² - 8

To find the inverse of any function we need to interchange the variables.

Hence, we get x = 2y² - 8

⇒ x = 2y² - 8

⇒ x + 8 = 2y²

⇒ (x + 8) / 2 = y²

⇒ √[(x + 8) / 2] = y

Therefore, √[(x + 8) / 2] is the inverse of y = 2x² - 8.