Question

If f(x)=x²,g(x)=3x and h(x)=x–2,Prove That (fog)oh=fo(goh)​

Answer 1

Answer:

Step-by-step explanation:

f(x) = x2 g(x) = 3x h(x) = x – 2 (fog)oh = x – 2 LHS = fo(goh) fog = f(g(x)) = f(3x) = (3x)2 = 9x (fog)oh = (fog) h(x) = (fog) (x – 2) = 9(x – 2)2 = 9(x2 – 4x + 4) = 9x2 – 36x + 36 … (1) RHS = fo(goh) (goh) = g(h(x)) = g(x – 2) = 3(x – 2) = 3x – 6 fo(goh) = f(3x – 6) = (3x – 6)2 = 9x2 – 36x + 36 … (2) (1) = (2) LHS = RHS (fog)oh = fo(goh) is proved