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$If f : R \to R and g : R \to R are given by f (x) = | x | and g (x) = [x] for each x \in R, then {x \in R : g (f (x)) \leq f (g (x))} =$

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Correct option is D

fx= x and gx =x ⇒gfx = gx =x and fgx=fx=x when x≥0 , x= x=x therefore gfx=fgx when x<0 , x≤x<0 since x≤x for all x x≥x≥x ⇒fgx≥gfx therefore gfx ≤fgx for all x∈R

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If f:R→R and g:R→R are given by f(x)=|x| and g(x)=[x] for each x∈R, then {x∈R:g(f(x))≤f(g(x))}=

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Ready to Test Your Skills?

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$If f : R \to R and g : R \to R are given by f (x) = | x | and g (x) = [x] for each x \in R, then {x \in R : g (f (x)) \leq f (g (x))} =$