If f(x) = x2, g(x) = 3x and h(x) = x – 2. Prove that (fog)oh = fo(go

1.	If f(x) = x2, g(x) = 3x and h(x) = x – 2. Prove that (fog)oh = fo(goh).
Answer» 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.

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

Answer»

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.