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

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

Options:

Correct Answer: The graph of a function and its inverse are symmetric about the line y = x.

Solution:

The graph of a function and its inverse are symmetric about the line y = x, which is a key property of inverse functions.

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

Which of the following statements is true regarding 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 function is f(x), the inverse is f⁻¹(y).
Step 3: Know what the line y = x represents. This line is where the x-coordinate and y-coordinate are equal.
Step 4: Realize that the graph of a function and its inverse will mirror each other across the line y = x. This means if you take a point (a, b) on the function, the point (b, a) will be on the inverse.
Step 5: Conclude that the symmetry about the line y = x is a key property of inverse functions.

No concepts available.