Exploring Inverse Functions and Their Graphs

What does the notation f^-1(x) represent in the context of functions?

• A function multiplied by -1

• A function raised to the power of -1

• The inverse of function f(x)

• None of the above

To find the inverse of the function f(x) = 2x - 5, what initial step should be taken?

• Switch x and y in the equation

• Add 5

• Subtract 5

• Divide by 2

When solving for the inverse, why is it important to use horizontal division symbols?

• To clearly indicate the numbers involved in the division

• To simplify the equation

• To avoid using parentheses

• To make the equation look neat

What must be done when an exponent involves a square in the function's equation?

• None of the above

• Add a square root

• Restrict the domain

• Multiply by 2

In the context of inverse functions, what does restricting the domain accomplish?

• Ensures the output is non-negative

• All of the above

• Prevents division by zero

• Makes the function one-to-one

How do you find the inverse of a function involving a cube operation?

• Take the square root

• Subtract the cube

• Take the cube root

• None of the above

What is the first step in finding the inverse of a function by swapping x and y?

• Isolate x

• Add constants to both sides

• Switch x and y in the equation

• Solve for y

What graphical feature is used to help visualize the relationship between a function and its inverse?

• A curved line

• A horizontal line

• A vertical line

• A diagonal line y = x

What happens to the points on a graph when finding the inverse of a function?

• They are halved

• They are squared

• They remain unchanged

• X and Y coordinates are swapped

Why should you not add arrows at the end of lines when plotting points for an inverse function graph?

• It indicates infinite continuation

• It suggests incorrect function behavior

• Arrows represent derivatives

• It is only used in vector graphics