Question

1. which of the following statements best describe an invertible function? select all that apply.

an invertible function is a function that has an inverse that is also a function.
an invertible function is said to be one - to - one.
an invertible function must pass the vertical and horizontal line test.
an invertible function must pass either the vertical or the horizontal line test.

Explanation:

1. For the first statement: By definition, an invertible function is a function for which the inverse relation is also a function. So this statement is correct.
2. For the second statement: A function is invertible if and only if it is one - to - one (injective). A one - to - one function means that no two different input values will produce the same output value. So this statement is correct.
3. For the third statement: The vertical line test is used to determine if a relation is a function. For a function to be invertible (and thus one - to - one), it must also pass the horizontal line test (which is used to determine if a function is one - to - one). So a function must pass both the vertical (to be a function) and horizontal (to be one - to - one) line tests to be invertible. This statement is correct.
4. For the fourth statement: A function must pass the vertical line test to be a function in the first place. And to be invertible, it must also be one - to - one (pass the horizontal line test). So it can't be either/or, it must be both. This statement is incorrect.

Answer:

• An invertible function is a function that has an inverse that is also a function.
• An invertible function is said to be one - to - one.
• An invertible function must pass the vertical and horizontal line test.