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Let [x] denote the integral part of x i...

Let [x] denote the integral part of `x in R and g(x) = x- [x]`. Let `f(x)` be any continuous function with `f(0) = f(1)` then the function `h(x) = f(g(x)` :

A

has finitely many discontinuities

B

is discontinuous at some x = c

C

is continuous on R

D

is a constant function

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The correct Answer is:
C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
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  3. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

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  4. Let f be a differentiable function on the open interval(a, b). Which o...

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  6. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

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  11. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

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  14. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

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  15. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

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  16. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

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  17. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

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  18. If x dy = y (dx + y dy), y > 0 and y (1) = 1, then y (−3) is equal t...

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  19. Let f(x) be continuous and differentiable function for all reals and f...

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  20. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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