Exploring Inverse Functions and Their Properties

What is the result when you apply an inverse function to the output of its original function?

• Zero

• The square of the original input

• A new unrelated number

• The input of the original function

If F(x) = x + 2, what is F inverse of x?

• x - 2

• x + 2

• 1/(x+2)

• 2 - x

What is the relationship between the domain of a function and the range of its inverse?

• There is no relationship

• They are identical

• The domain of one is the range of the other

• They are inversely proportional

How do you find the inverse of a function algebraically?

• By subtracting the original function from one

• By swapping the variables and solving for the new variable

• By taking the square root of the original function

• By dividing by the original function

What must be true for a function to have an inverse?

• It must be a polynomial of degree 2 or higher

• It must be a linear function

• It must be possible to solve for the variable after swapping

• It must pass the vertical line test

Why can't some functions have inverses?

• Because they are not continuous

• Because they are too complex

• Because they don't pass the horizontal line test

• Because they can't be solved for the variable after swapping

How can you verify that two functions are inverses of each other?

• By subtracting one from the other

• By adding them together

• By dividing one by the other

• By applying one after the other and checking if the input is retrieved

For the function F(x) = 4x - 5, what is the correct inverse function?

• (x + 5) / 4

• 4 / (x - 5)

• (x - 5) / 4

• 4x + 5

What is the inverse of F(x) = x^3 + 1?

• The cube root of (x - 1)

• The cube root of (x + 1)

• x^3 - 1

• (x - 1)^3

What happens to the graph of a function when you reflect it across the line y = x?

• You get its inverse function

• The graph remains unchanged

• You get a completely unrelated graph

• The graph becomes a straight line