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 — missed you this week. Here are the solutions for question 12: Given the functions p(x) = (3)/(x-2) and q(x) = x+1. a) Find pq(x) Step 1: To find pq(x), we substitute q(x) into p(x). This means we replace every x in p(x) with the expression for q(x). pq(x) = p(q(x)) = p(x+1) Step 2: Substitute x+1 into p(x) = (3)/(x-2). p(x+1) = (3)/((x+1)-2) Step 3: Simplify the denominator. p(x+1) = (3)/(x-1) The expression for pq(x) is (3)/(x-1). b) Find qp(x) Step 1: To find qp(x), we substitute p(x) into q(x). This means we replace every x in q(x) with the expression for p(x). qp(x) = q(p(x)) = q((3)/(x-2)) Step 2: Substitute (3)/(x-2) into q(x) = x+1. q((3)/(x-2)) = (3)/(x-2) + 1 Step 3: Combine the terms by finding a common denominator. q((3)/(x-2)) = (3)/(x-2) + (1(x-2))/(x-2) q((3)/(x-2)) = (3 + x - 2)/(x-2) Step 4: Simplify the numerator. q((3)/(x-2)) = (x+1)/(x-2) The expression for qp(x) is (x+1)/(x-2). Send me the next one 📸