To determine the set A for which the function f: R A defined as f(x) = x2 + 1 is onto, we need to find the range of the function f(x).

To determine the set A for which the function f: R A defined as f(x) = x^2 + 1 is onto, we need to find the range of the function f(x). Step 1: Analyze the expression for f(x). The function is given by f(x) = x^2 + 1. Step 2: Determine the range of f(x). For any real number x, we know that x^2 0. Adding 1 to both sides of the inequality, we get: x^2 + 1 0 + 1 x^2 + 1 1 This means that the minimum value of f(x) is 1, and f(x) can take any value greater than or equal to 1. Therefore, the range of f(x) is [1, ). Step 3: Identify the set A for an onto function. For a function f: R A to be onto (or surjective), its codomain A must be equal to its range. Since the range of f(x) = x^2 + 1 is [1, ), the set A must be [1, ) for the function to be onto. Step 4: Compare with the given options. The options are: a) (-, ) b) (-, 1] c) [1, ) d) [1, ) The correct option is c) or d). The final answer is c) [1, ). Send me the next one 📸