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Question
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x2 + 2x − 3 and g(x) = 3x − 4 .
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Solution
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = x2 + 2x − 3 and g(x) = 3x − 4
(gof) (x)
= g (f(x))
= g ( x 2+2x−3 )
= 3 (x2+2x−3) −4
= 3x2+ 6x − 9 − 4
= 3x2+6x−13
(fog) (x)
= f (g (x))
= f (3x−4)
= (3x − 4) 2+2 ( 3x − 4) −3
= 9x2+16−24x+6x−8−3
= 9x2−18x + 5
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