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Question
Find fog and gof if : f(x) = c, c ∈ R, g(x) = sin `x^2`
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Solution
f (x) = c, g (x) = sin x2
f : R → {c} ; g : R→ [ 0, 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 x2)
= c
Computing gof :
Clearly, the range of f is a subset of the domain of g.
⇒ fog : R→ R
(gof) (x) = g (f (x))
= g (c)
= sin c2
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