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Let f (x) =[x] and g (x) =0 when x is an...

Let `f (x) =[x] and g (x) =0` when x is an integer and `g (x) =x ^(2)` when x is not an integer ([] is ghe greatest integer function) then:

A

`lim _(xto1) g(x)` exists, but g (x) is not continous at `x=1`

B

`lim _(xto1) f (x)` does not exist

C

gog is continous for all x

D

fog is continous for all x

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The correct Answer is:
A, B
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VIKAS GUPTA (BLACK BOOK)-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  6. Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:

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  12. Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...

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  13. If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...

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  14. If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...

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  16. Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt...

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  17. Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...

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  18. f (x) is differentiable function satisfying the relationship f ^(2) (x...

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