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Suppose a function f(x) satisfies the fo...

Suppose a function f(x) satisfies the following conditions
`f (x+y) =(f(x) +f(y))/(f +f(x) f(y))' AA x , y in R and f '(0)=1`
Also `-1lt f (x) lt 1, AA x in R`
f(x) increases in the complete interval :

A

`(-oo, -1) uu (-1,0) uu (0,1) uu (1,oo)`

B

`(-oo, oo)`

C

`(-oo, 1)uu (-1, 0)`

D

`(0,1)uu (1,oo)`

Text Solution

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The correct Answer is:
B
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VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  2. Let f :R to R be a continous and differentiable function such that f (...

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  3. Let f :R to R be a continous and differentiable function such that f (...

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  4. Let f :R to R be a continous and differentiable function such that f (...

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  5. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

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  6. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

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  7. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  8. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  9. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  10. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  11. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  12. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  13. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  14. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  15. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  16. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  17. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

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  18. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

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  19. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

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  20. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

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