Question

if f(x)=x2,g(x)=2x and h(x)=x+4 then prove that fo(goh)=(fog)oh​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Proof:

Prerequisites:

fog represents the composite class of function which implies that:

$fog \equiv f(g(x))$ i.e, g(x) itself is the input for f(x)

Given

$f(x) = x^2\\g(x) = 2x\\h(x) = x+4$

Let's calculate:

$fog = f(2x) = (2x)^2 = 4x^2\\goh = g(x+4) = 2(x+4) = 2x+8\\\\\implies fo(goh) = f(2x+8) \\\implies fo(goh) = (2x+8)^2 = 4x^2 +32x+64\\\\\implies (fog)oh = (fog) (x+4) = 4 (x+4)^2 = 4x^2 +32x+64\\\\\implies fo(goh) = (fog)oh$

LHS = RHS

Hence proved.

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