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Question
Find fog and gof if : f (x) = x+1, g (x) = sin x .
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Solution
f(x) = x+1, g(x) = sin x
f : R→R ; g : R→[−1, 1]
Computing fog :
Clearly, the range of g is a subset of the domain of f.
⇒ fog: R→ R
(fog) (x) = f (g (x))
= f ( sin x )
= sin x + 1
Computing gof:
Clearly, the range of f is a subset of the domain of g.
⇒ fog : R → R
(gof) (x) = g (f (x))
= g (x+1)
= sin ( x+1)
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