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If f:R-{-1}toR and f is differentiable f...

If `f:R-{-1}toR and f` is differentiable function satisfies:
`f((x)+f(y)+xf(y))=y+f(x)+yf(x)AAx,`
`yinR-{_1}` Find f(x).

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=(-x)/(1+x)`
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ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f:R-{-1}toR and f is differentiable function satisfies: f((x)+f(y...

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  2. A solution curve of the differential equation (x^2+xy+4x+2y+4)((dy)/(d...

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  3. Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(...

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  4. Let y(x) be a solution of the differential equation (1+e^(x))y^(')+ye^...

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  5. Let y(x) be a solution of the differential equation (1+e^(x))y'+ye^(x)...

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  6. Solve the differential equation : y sqrt(1-x^2)dy-sqrt(1+y^2)dx=0

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  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  8. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

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  9. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  10. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  11. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  12. Consider the statements : P : There exists some x IR such that f(x)...

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  13. Differentiate the following w.r.t x (log x)^(cos x)

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  14. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  15. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  16. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  17. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  18. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  19. Let the population of rabbits surviving at a time t be governed by t...

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  20. At present, a firm is manufacturing 2000 items. It is estimated tha...

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