This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Here are the steps to solve the given problem: We are given the following functions: F(x) = 2x+3 g(x) = x-1 We need to find F(2), g^-1(x), and fg(x). Step 1: Calculate F(2) To find F(2), we substitute x=2 into the expression for F(x). F(2) = 2(2) + 3 F(2) = 4 + 3 F(2) = 7 The value of F(2) is 7. Step 2: Find g^-1(x) To find the inverse function g^-1(x), we set y = g(x), then swap x and y and solve for y. Let y = x-1. Swap x and y: x = y-1 Now, solve for y: y = x+1 So, the inverse function is g^-1(x) = x+1. The inverse function of g(x) is g^-1(x) = x+1. Step 3: Find fg(x) The notation fg(x) represents the composition of functions F(g(x)). We substitute the expression for g(x) into F(x). fg(x) = F(g(x)) We know that g(x) = x-1. fg(x) = F(x-1) Now, we substitute (x-1) in place of x in the expression for F(x) = 2x+3: fg(x) = 2(x-1) + 3 fg(x) = 2x - 2 + 3 fg(x) = 2x + 1 The composite function fg(x) is fg(x) = 2x+1. Send me the next one 📸