This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
It seems there might be a slight misunderstanding in the notation. For the function f(x) = x^2, we are looking for f(x+h), not f(x+h)^2. Here's how we get f(x+h): Step 1: Understand the function definition. The function is defined as f(input) = (input)^2. Whatever is inside the parentheses of f(·) gets squared. Step 2: Substitute (x+h) as the input. When we want to find f(x+h), we replace every instance of x in the original function f(x) = x^2 with (x+h). So, f(x+h) = (x+h)^2. Step 3: Expand the expression (x+h)^2. This is a standard algebraic expansion: (x+h)^2 = (x+h)(x+h) (x+h)^2 = x · x + x · h + h · x + h · h (x+h)^2 = x^2 + xh + xh + h^2 (x+h)^2 = x^2 + 2xh + h^2 So, f(x+h) is equal to x^2 + 2xh + h^2. What's next? 📸