How to find the inverse of a quadratic that is a function

The video tutorial explains how to find the inverse of a quadratic function, h(x) = 5x^2 + 12. The process involves replacing h(x) with y, swapping x and y, and using inverse operations to solve for y. The tutorial highlights the importance of applying constraints to ensure the inverse function is valid, focusing on the positive square root and setting x to be greater than or equal to 12 to avoid negative radicands.

What is the first step in finding the inverse of the function h(x) = 5x^2 + 12?

• Replace h(x) with y

• Multiply by 5

• Swap x and y

• Add 12 to both sides

Which operation is used to undo the multiplication by 5 when solving for y?

• Division

• Square root

• Subtraction

• Addition

What is the expression for y after taking the square root of both sides?

• y = x - 12

• y = 5(x - 12)

• y = (x - 12) / 5

• y = ±√((x - 12) / 5)

Why is a constraint placed on the value of x in the inverse function?

• To ensure x is always positive

• To prevent the radicand from being negative

• To make the function linear

• To simplify the equation

What is the constraint placed on x for the inverse function to be valid?

• x must be a negative number

• x must be equal to 12

• x must be less than 12

• x must be greater than or equal to 12