Final answer:
When x = 0, the function f(x) {x^2: x ≤ 1, 2x+1: x > 1} uses the expression x^2, thus the correct function to use is A. x^2. The value of the function at x = 0 is A. 0 since 0 squared is 0.
Step-by-step explanation:
To identify the appropriate function for a given value of x, we need to look at the defined intervals for the function. f(x) is a piecewise-defined function with two expressions, and the relevant expression is chosen based on the value of x. Given our expression f(x) {x^2: x ≤ 1, 2x+1: x > 1}, we need to decide which part of the function to use when x = 0. Part 1: Identify the function that will be used when x = 0. Since x = 0 is less than or equal to 1, we will use the first part of the function, which is x^2. So, the correct option is A. x^2. Part 2: Find the value of the function when x = 0. Using the expression x^2 for x = 0, we calculate the value of the function: f(0) = 0^2 = 0. Therefore, the value of the function when x = 0 is: A. 0