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Question
If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?
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Solution
We know that
f : R→ [−1, 1] and g : R→ R
Clearly, the range of f is a subset of the domain of g.
gof : R→ R
(gof) (x) = g (f (x))
= g ( sin x)
= 2 sin x
Clearly, the range of g is a subset of the domain of f.
fog : R → R
So, (fog) (x) = f (g (x))
= f (2x)
= sin (2x)
Clearly, fog ≠ of
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