Q. 65.0( 1 Vote )

Let f, g, h be real functions given by f(x) = sin x, g(x) = 2x and h(x) = cos x. Prove that fog = go(fh).

Answer :

f, g and h are real functions given by f(x) = sin x, g(x) = 2x and


h(x) = cos x


To prove: fog=go(fh)


L.H.S


fog(x) = f(g(x))


= f(2x) = sin 2x


fog(x)=2sin x cos x ……(A)


R.H .S


go(fh)(x) = go(f(x).h(x))


= g(sin x cos x) = 2sin x cos x


go(fh)(x) = 2 sin x cos x ……(B)


from A and B


fog(x) = go(fh)(x)


Hence proved


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