Question:
if f (x) =sinx,g(x) =cosx and h(x) and 2x,h,g and f are the real value functions .show that ho(fg)= foh
Answer:
Given,
f(x) = sin x
g(x) = cos x
h(x) = 2x
Now, fog(x) = f(g(x))
= f(cos x)
= sin (cos x)
Now, hofog(x) = h{fog(x)}
= h(sin (cos x))
= 2sin (cos x)
Again,
foh(x) = f(h(x))
= f(2x)
= sin (2x)
= 2*sin x*cos x
So, hofog(x) ≠ foh(x)
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