Which of the following statements is true about the inverse of a function?

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Question: Which of the following statements is true about the inverse of a function?

Options:

Correct Answer: The inverse of a function is not necessarily a function.

Solution:

The inverse of a function is a function only if the original function is one-to-one.

Which of the following statements is true about the inverse of a function?

Which of the following statements is true about the inverse of a function?

Step 1: Understand what a function is. A function takes an input and gives an output based on a specific rule.
Step 2: Learn about the inverse of a function. The inverse of a function reverses the input and output. If the original function is f(x), the inverse is f⁻¹(y).
Step 3: Know what 'one-to-one' means. A function is one-to-one if different inputs always give different outputs. This means no two inputs can produce the same output.
Step 4: Realize that for a function to have an inverse that is also a function, it must be one-to-one. If it is not one-to-one, the inverse will not pass the vertical line test (which checks if a relation is a function).
Step 5: Conclude that the statement is true: The inverse of a function is a function only if the original function is one-to-one.

No concepts available.