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
Step 1: Substitute (a+1) into the function h(x) = 3x^2. We are given the function h(x) = 3x^2. To find h(a+1), we replace x with (a+1): h(a+1) = 3(a+1)^2 Step 2: Use the given condition h(a+1) = 3. We are told that h(a+1) = 3. So, we can set the expression from Step 1 equal to 3: 3(a+1)^2 = 3 Step 3: Solve the equation for a. Divide both sides by 3: (a+1)^2 = (3)/(3) (a+1)^2 = 1 Take the square root of both sides. Remember to consider both positive and negative roots: a+1 = ±sqrt(1) a+1 = ± 1 This gives two possible cases: Case 1: a+1 = 1 Subtract 1 from both sides: a = 1 - 1 a = 0 Case 2: a+1 = -1 Subtract 1 from both sides: a = -1 - 1 a = -2 The values of a are 0 and -2. The value of a is 0 or -2.