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Question
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 8x3 and g(x) = x1/3.
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Solution
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = 8x3 and g(x) = x1/3
(gof) (x)
= g (f (x))
= g (8x3)
=`(8x^3)^(1/3)`
= `[(2x)^3]^(1/3)`
= 2x
(fog) (x)
= f (g (x))
=` f (x^(1/3))`
=` 8 (x^(1/3))^3`
= 8x
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