Question

# Suppose that f is a function that is defined for all real numbers. Which of the following conditions assures that f has an inverse function? a. The graph off is concave up. b. The graph of f is symmetric with respect to they-axis. c. The function f is a strictly increasing function. d. The function f is continuous.

Answer

The function f has an inverse if and only if it is a one-to-one function. The condition that assures that f has an inverse function is c. The function f is a strictly increasing function.

- Q: What does it mean for a function to have an inverse? A: A function has an inverse if and only if it is a one-to-one function.
- Q: What is a one-to-one function? A: A function is one-to-one if each element in the range of the function corresponds to exactly one element in the domain of the function.
- Q: Which of the given conditions provide for a one-to-one function? A: The condition that assures that f has an inverse function is c. The function f is a strictly increasing function.