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Question
Find fog and gof if : f(x)= x + 1, g (x) = 2x + 3 .
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Solution
f (x) = x+1, g (x) = 2x + 3
f : R→R ; g : R → R
Computing fog :
Clearly, the range of g is a subset of the domain of f.
⇒ fog : R→ R
(fog) (x) = f (g (x))
= f (2x+3)
= 2x + 3 + 1
= 2x + 4
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)
= 2 ( x + 1) + 3
= 2x + 5
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