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Question
Find fog and gof if : f (x) = |x|, g (x) = sin x .
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Solution
f (x) = |x|, g(x) = sin x
f : R → (0, ∞) ; 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|
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|)
= sin |x|
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