Understanding Functions and Their Inverses

The video tutorial explains the concept of one-to-one functions and their inverses. It highlights how a function and its inverse undo each other, using examples to demonstrate this relationship. The tutorial shows that if F of 2 equals 5, then F inverse of 5 equals 2, illustrating the switch in coordinates. It also explains the symmetry of the graphs of a function and its inverse across the line y = x. A second example is provided to reinforce the understanding of these concepts.

What is a one-to-one function?

• A function that is always increasing

• A function that has the same output for different inputs

• A function that has an inverse function

• A function that is not defined for all real numbers

If f(x) = y, what happens when y is input into the inverse function?

• The output is undefined

• The output is x

• The output is always zero

• The output is y

In the example where f(2) = 5, what is f inverse of 5?

• 2

• 5

• 0

• Undefined

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

• They are switched

• They are halved

• They are identical

• They are doubled

Why are the graphs of a function and its inverse symmetrical across the line y = x?

• Because they are both linear

• Because they have the same domain

• Because they have the same range

• Because their coordinates are switched

In the second example, if f inverse of -3 = -2, what is f of -2?

• -2

• -3

• 3

• 0

What does the point (-3, -2) in the inverse function tell us about the original function?

• It contains the point (-3, -2)

• It contains the point (-2, -2)

• It contains the point (-3, -3)

• It contains the point (-2, -3)

What is the key takeaway about the relationship between a function and its inverse?

• They are unrelated

• They undo each other

• They are always different

• They are always equal

How do the initial input and final output relate in a function and its inverse?

• They are doubled

• They are halved

• They are the same

• They are always different

What does the symmetry across the line y = x indicate about a function and its inverse?

• They have switched coordinates

• They are perpendicular

• They have the same slope

• They are parallel