Understanding Inverses of Functions

What is the first step in finding the inverse of a function?

• Switch x and y

• Solve for x

• Add 1 to both sides

• Replace f(x) with y

When finding the inverse of a cubic function, what is the relationship between the original and inverse functions?

• They are identical

• They are mirror images over y = x

• They have the same domain

• They have the same range

What is the domain and range of a cubic function?

• 0 to infinity

• Negative infinity to infinity

• 1 to 10

• Negative 10 to 10

What is the opposite operation of taking a cube root?

• Squaring

• Cubing

• Taking a square root

• Adding 2

In the context of cube root functions, what does the reflection over y = x imply?

• The function is constant

• The function is quadratic

• The function is linear

• The function and its inverse are mirror images

What new concept is introduced when dealing with square roots and quadratics?

• Complex numbers

• Linear functions

• Inverse operations

• Domain restrictions

How do you eliminate a square root when finding an inverse?

• Add 1 to both sides

• Cube both sides

• Subtract 3 from both sides

• Square both sides

What is the domain of a quadratic function when considering its inverse?

• Negative 5 to infinity

• 0 to infinity

• 3 to infinity

• Negative infinity to infinity

Why can only half of a quadratic be used to find its inverse?

• To ensure it is a function

• To make it linear

• To simplify calculations

• To avoid complex numbers

What is the significance of the vertex in determining the domain and range of a quadratic's inverse?

• It affects the color of the graph

• It defines the starting point

• It is irrelevant

• It determines the slope