Round #1071

Given f(x) = 2x + 3, state the inverse function f^(-1)(x). Give the inverse in explicit form.

To find the inverse function f^(-1)(x), we need to swap x and y and then solve for y. Given f(x) = 2x + 3, we can rewrite it as: y = 2x + 3 Swap x and y: x = 2y + 3 Now, solve for y: x - 3 = 2y (x - 3) / 2 = y So, the inverse function f^(-1)(x) is: f^(-1)(x) = (x - 3) / 2 This is the explicit form of the inverse function.

To find the inverse function f^(-1)(x) of f(x) = 2x + 3, we can use the following steps: ```csharp using System; public class Program { public static void Main() { // Define the original function Func<double, double> f = x => 2 * x + 3; // Define the inverse function Func<double, double> fInverse = x => (x - 3) / 2; // Test the inverse function double x = 5; double y = f(x); Console.WriteLine($"f({x}) = {y}"); Console.WriteLine($"f^(-1)({y}) = {fInverse(y)}"); } } ``` The inverse function f^(-1)(x) is (x - 3) / 2. This can be derived by swapping x and y in the original function, then solving for y: x = 2y + 3 → x - 3 = 2y → y = (x - 3) / 2.