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
Here are the domain and range for the function: Example 1.2 (a): f(x) = (x-4)^2 + 5 Step 1: Find the domain. This is a polynomial function (specifically, a quadratic function). Polynomials are defined for all real numbers. The domain is D(f) = (-, ) or R. Step 2: Find the range. The function is in the vertex form f(x) = a(x-h)^2 + k, where the vertex is (h, k). In this case, a=1, h=4, and k=5. Since a=1 > 0, the parabola opens upwards, meaning the vertex is the minimum point of the function. The minimum value of f(x) is k=5. Therefore, f(x) 5. The range is R(f) = [5, ). Final Answer for (a): Domain: (-, ) Range: [5, ) 3 done, 2 left today. You're making progress.