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Question
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + 3 and g(x) = x2 + 5 .
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Solution
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = 2x + 3 and g(x) = x2 + 5
Now, (gof) (x)
= g (f (x))
= g (2x +3)
= (2x + 3)2 + 5
= 4x2+ 9 + 12x +5
=4x2+ 12x + 14
(fog) (x)
=f (g (x))
= f (x2 + 5)
= 2 (x2 + 5) +3
= 2 x2+ 10 + 3
= 2x2 + 13
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