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: Identify the correct interval for x=6. The given piecewise function is: f(x) = -2x - 2 & if x -5 \\ 2x^2 + 2x & if -5 < x 5 \\ (3)/(4)x - 1 & if x > 5 For x=6, we check which condition it satisfies: • 6 -5 is false. • -5 < 6 5 is false. • 6 > 5 is true. So, we use the third expression: f(x) = (3)/(4)x - 1. Step 2: Substitute x=6 into the chosen expression. f(6) = (3)/(4)(6) - 1 Step 3: Calculate the value. f(6) = (18)/(4) - 1 \\ f(6) = (9)/(2) - 1 \\ f(6) = (9)/(2) - (2)/(2) \\ f(6) = (7)/(2) The value of the function at x=6 is (7)/(2). 3 done, 2 left today. You're making progress.