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

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

Options:

The inverse of a function is always a function.
The inverse of a function is symmetric to the original function about the line y = x.
The inverse can only exist for polynomial functions.
The inverse of a function is always linear.

Correct Answer: The inverse of a function is symmetric to the original function about the line y = x.

Solution:

The inverse of a function is symmetric to the original function about the line y = x, provided the original function is one-to-one.

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

The inverse of a function is always a function.
The inverse of a function is symmetric to the original function about the line y = x.
The inverse can only exist for polynomial functions.
The inverse of a function is always linear.

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

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 function reverses the roles of inputs and outputs. If the original function is f(x), the inverse is f⁻¹(y).
Step 3: Know what 'one-to-one' means. A one-to-one function means that each input has a unique output, and no two different inputs produce the same output.
Step 4: Understand the line y = x. This line represents points where the input and output are equal. For example, (1,1) and (2,2) are points on this line.
Step 5: Learn about symmetry. If a function and its inverse are symmetric about the line y = x, it means that if you were to fold the graph along this line, the two graphs would match up.
Step 6: Conclude that if the original function is one-to-one, then its inverse will be symmetric to the original function about the line y = x.

No concepts available.