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: Use the definition of composite functions. Given f g(x) = (x+2)/(3) and g(x) = 2x+5. The notation f g(x) means f(g(x)). So, we have: f(g(x)) = (x+2)/(3) Step 2: Substitute the expression for g(x) into the equation. f(2x+5) = (x+2)/(3) Step 3: Find the expression for f(x). Let u = 2x+5. We need to express x in terms of u. u = 2x+5 u-5 = 2x x = (u-5)/(2) Now substitute this expression for x into the equation for f(2x+5): f(u) = ((u-5)/(2))+23 Simplify the numerator: f(u) = (u-5+4)/(2)3 f(u) = (u-1)/(2)3 f(u) = (u-1)/(6) Replacing u with x, we get the function f(x): f(x) = (x-1)/(6) Step 4: Find the value of f(x+1). Substitute (x+1) into the expression for f(x): f(x+1) = ((x+1)-1)/(6) f(x+1) = (x)/(6) The value of f(x+1) is (x)/(6). Send me the next one 📸