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Let f: RvecR be a function satisfying co...

Let `f: RvecR` be a function satisfying condition `f(x+y^3)=f(x)+[f(y)]^3fora l lx ,y in Rdot` If `f^(prime)(0)geq0,` find `f(10)dot`

A

f(x) = 0 only

B

f(x) = x only

C

f(x) = 0 or x only

D

f(10) = 10

Text Solution

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The correct Answer is:
C, D
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ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. about to only mathematics

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  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

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  7. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

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  11. In the following, [x] denotes the greatest integer less than or equal ...

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  13. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

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  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  16. The left hand derivative of f(x)=[x]sin(pix) at x = k, k in Z, is

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  17. Which of the following functions is differentiable at x = 0?

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  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

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  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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