InterviewSolution
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InterviewSolution
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Find gof and fog, if `f : R ->R`and `g : R ->R`are given by `f(x) = cos x`and `g(x)=3x^2`. Show that `gof!=fog`. |
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Answer» Let x be an arbitrary real number . Then `(g o f) (x) =g {f (x)} =g (cos x) =3 (cos x)^(2) =3 cos ^(2) x.` `(f o g) (x) =f {g (x)}= f(3x^(2)) ` Taking x=0 , we have (g o f) (0) `=3 cos^(2) 0 =(3 xx 1) =3` `(f o g) (0) =cos (3 xx 0) =cos 0=1` `:. (g o f) (0) ne (f o g) (0)` Hence g o f` ne ` f og |
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