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Question
Find fog and gof if : f (x) = ex g(x) = loge x .
Solution
f (x)=ex, g(x) = loge x
f : R → ( 0, ∞); g : ( 0, ∞) → R
Computing fog:
Clearly, the range of g is a subset of the domain of f.
fog : ( 0, ∞) → R
(fog) (x) = f (g (x))
= f (loge x)
= loge ex
= 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 (ex)
= loge ex
= x
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