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Question
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x2 + 8 and g(x) = 3x3 + 1 .
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Solution
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = x2 + 8 and g(x) = 3x3 + 1
(gof) (x)
= g ( f (x))
= g ( x2 + 8 )
= 3 ( x 2+8 )3 + 1
(fog) (x)
= f ( g ( x ))
= f ( 3x3 + 1 )
= ( 3x3+1 )2 + 8
= 9x6 + 6x3+ 1+ 8
=9x6+6x3+9
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