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Let f(x) = 1/2[f(xy) + f(x/y)] for x,y i...

Let `f(x) = 1/2[f(xy) + f(x/y)]` for `x,y in R^+` such that f(1) = 0
f'(1) = 2
Answer the following question based on above passage :
f€ is equal to

A

2

B

1

C

3

D

4

Text Solution

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The correct Answer is:
A
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PATHFINDER-FUNCTION-QUESTION BANK
  1. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  2. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  3. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  4. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  5. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  6. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  7. Match List - I with List-II

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  8. Match List - I with List-II

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  9. Let f(x) be function such that f(x + 2)- 5f(x + 1) + 6f(x) = 0 AA x in...

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  10. Match List - I with List-II

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  11. If maximum and minimum value of f(x)=^xC(2x-1)+^(20-3x)C(4x-5) are la...

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  12. Let f be the function from the set of positive integers to the set of ...

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  13. The least period of the function sin((x[x])/12)+cos((nx)/4)+tan((pi(x)...

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  14. If maximum and minimum value of f(x)=^xC(2x-1)+^(20-3x)C(4x-5) are la...

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  15. If the period of the function cos(nx)sin((5x)/n) is 3pi,then the numb...

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  16. If f(x+y)=f(x)+f(y)-xy-1' for all x,y in Rand f(1)=1,then the value of...

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  17. Let n(A)=4 and n(B)=6 ,then the number of one one functions from A to ...

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  18. If f(x)f(y)+2=f(x)+f(y)+f(xy) AA x,y in R and f(1)=f'(1)=2, then sgn (...

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  19. Let f:[0,1]rarr[0,1] defined by f(x)=(1-x)/(1+x)for0lexle1 and let g:...

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  20. If f(x)=1+x^2and f(g(x))=1+x^2-x^3+x^4,g(2)=2,then g(3) equals

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