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 solutions to the problems. Problem 1: If f(x) = (1)/(x+1), find f(x-1). Step 1: Substitute (x-1) for x in the function f(x). f(x-1) = (1)/((x-1)+1) Step 2: Simplify the expression. f(x-1) = (1)/(x) The function f(x-1) is: (1)/(x) Problem 2: Integrate the function y = 3x^2 + 2x + 5 with respect to x. Step 1: Set up the integral. (3x^2 + 2x + 5)\,dx Step 2: Apply the power rule for integration x^n\,dx = x^n+1n+1 + C to each term. 3x^2\,dx + 2x\,dx + 5\,dx = 3(x^2+12+1) + 2(x^1+11+1) + 5x + C = 3((x^3)/(3)) + 2((x^2)/(2)) + 5x + C Step 3: Simplify the expression. = x^3 + x^2 + 5x + C The integral of the function is: x^3 + x^2 + 5x + C