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Let R be the set of all real numbers. Le...

Let R be the set of all real numbers. Let `f: R rarr R ` be a function such that : `|f(x) - f(y)|^2 le |x-y|^2, AA x, y in R ` . Then f(x) =

A

x

B

1

C

0

D

`x^2`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
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  8. If y=(1+x)(1+x^2)(1+x^4), then dy/dx at x = 1 is

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  13. Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and ...

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  14. If 'f' is differentiable at x = a, find (underset(xrarra)lim(x^2f(a)-a...

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  15. If f: R rarr R is a function defined by: f(x) = [x] cos((2x-1)/2)pi, ...

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  16. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  18. If g is te inverse of a function f and f'(x) = 1/(1+x^5) then g'(x) is...

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  19. If the function g(x) = {{:(k sqrt(x + 1)",", 0 le x le 3),(mx + 2",",3...

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  20. For x in R, f(x) = |log 2 - sin x| and g(x) = f(f(x)), then

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