F(x)=3x-2 and g (x)=x²+2x-3 solve and show solution

Step-by-step explanation:Solve and analyze the two functions step by step:Given:1. Evaluate :This means substitute into .So,f(g(x)) = f(x^2 + 2x - 3)Now plug this into , replacing x with :f(g(x)) = 3(x^2 + 2x - 3) - 2Distribute the 3:= 3x^2 + 6x - 9 - 2= 3x^2 + 6x - 11✅ Final answer:f(g(x)) = \boxed{3x^2 + 6x - 11}---2. Evaluate :This time, substitute into :g(f(x)) = g(3x - 2)Now plug into , replacing x with :g(f(x)) = (3x - 2)^2 + 2(3x - 2) - 3First, expand := 9x^2 - 12x + 4Next, expand := 6x - 4Now combine everything:g(f(x)) = 9x^2 - 12x + 4 + 6x - 4 - 3Combine like terms:= 9x^2 - 6x - 3✅ Final answer:g(f(x)) = \boxed{9x^2 - 6x - 3}

Answered by romnickpallon | 2025-07-03