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
Welcome back Baby — been a while! Let's pick up where you left off. To find (f g)(x), we need to substitute g(x) into f(x). Step 1: Identify the given functions. We have f(x) = x^2 - 1 and g(x) = sqrt(x) + 1. Step 2: Substitute g(x) into f(x). The notation (f g)(x) means f(g(x)). Substitute g(x) into the expression for f(x): f(g(x)) = f(sqrt(x) + 1) Replace x in f(x) with (sqrt(x) + 1): f(sqrt(x) + 1) = (sqrt(x) + 1)^2 - 1 Step 3: Expand the expression. Expand (sqrt(x) + 1)^2 using the formula (a+b)^2 = a^2 + 2ab + b^2: (sqrt(x) + 1)^2 - 1 = ((sqrt(x))^2 + 2(sqrt(x))(1) + 1^2) - 1 = (x + 2sqrt(x) + 1) - 1 Step 4: Simplify the expression. x + 2sqrt(x) + 1 - 1 = x + 2sqrt(x) Step 5: Compare with the given options. The simplified expression is x + 2sqrt(x). This matches option A. The final answer is A. x + 2sqrt(x). Send me the next one 📸