Understanding Inverse Functions

The video tutorial explains how to find the inverse of a given function, h(x) = -∛(3x - 6) + 12. It begins by introducing the concept of inverse functions and how they map from a range back to a domain. The tutorial then walks through the algebraic steps to solve for the inverse function, including isolating terms, manipulating equations, and finalizing the inverse expression. The video emphasizes understanding the process of reversing a function's operations to find its inverse.

What is the main goal when finding the inverse of a function?

• To find a function that doubles the input

• To find a function that maps from the domain to the range

• To find a function that squares the input

• To find a function that maps from the range back to the domain

What is one method to find the inverse of a function?

• Swap x and y, then solve for y

• Multiply the function by 2

• Add 10 to the function

• Divide the function by 3

What is the first step in isolating the cube root when finding the inverse?

• Divide by 3

• Multiply by 2

• Subtract 12 from both sides

• Add 12 to both sides

Why do we multiply both sides by negative one during the process?

• To eliminate the negative sign in front of the cube root

• To make the equation more complex

• To simplify the cube root

• To add a negative sign to the cube root

What operation is performed after isolating the cube root?

• Subtract 6 from both sides

• Add 5 to both sides

• Cube both sides

• Square both sides

What is the result of cubing both sides of the equation?

• The cube root is eliminated

• The equation becomes quadratic

• The equation becomes linear

• The equation becomes exponential

What is the final step in expressing the inverse function?

• Multiply by 3

• Subtract 12

• Add 12

• Divide by 3

What flexibility do we have when naming the input variable in the inverse function?

• It must always be called x

• It must always be called z

• We can name it anything we like

• It must always be called y

What does the inverse function essentially do?

• Squares the output of the original function

• Halves the output of the original function

• Doubles the output of the original function

• Unwinds what the original function does

What is the expression for the inverse function h inverse of x?

• 12 minus x cubed plus six over three

• x cubed minus 12 plus six over three

• 12 plus x cubed minus six over three

• x cubed plus 12 minus six over three