Home
Class 12
MATHS
Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R ...

Let `f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R` and `f(0)=k`, then

A

`f(2)+f(-2)=0`

B

`f(3)+f(-3)=0`

C

`f^'(2)+f^'(-2)=0`

D

`f^'(3)+f^1(-3)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Recent IIT questions

    A DAS GUPTA|Exercise Exercise|20 Videos
  • Some New Pattern Problems

    A DAS GUPTA|Exercise Exercise|137 Videos

Similar Questions

Explore conceptually related problems

If f satisfies the relation f(x+y)+f(x-y)=2f(x)f(y)AA x,y in K and f(0)!=0; then f(10)-f(-10)-

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

Let a real valued function f satisfy f(x+y)=f(x)f(y)AA x,y in R and f(0)!=0 Then g(x)=(f(x))/(1+[f(x)]^(2)) is

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

Let f(x+y)=f(x)*f(y)AA x,y in R and f(0)!=0* Then the function phi defined by .Then the function phi(x)=(f(x))/(1+(f(x))^(2)) is

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)AA x,y in R and if f(2)=5, then find the value of f(f(2))

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^(2)y-y^(3))AA x,y in R and f(1)=2 ,then

Let f(x+(1)/(y))+f(x-(1)/(y))=2f(x)f((1)/(y))AA x,y in R,y!=0 and f(0)=0 then the value of f(1)+f(2)=

A DAS GUPTA-Screening Tests-Exercise
  1. If log30(3)=alpha and log30(5)=beta, then log30(8) is equal to

    Text Solution

    |

  2. An infinite G.P has first term x and sum 5 then x belongs to ?

    Text Solution

    |

  3. The number of ways of distributing 8 identical balls in 3 distinct box...

    Text Solution

    |

  4. The coefficient of the middle term in the binomial expansion in powers...

    Text Solution

    |

  5. If (n-1)Cr=(k^2-3)nC(r+1),then k belong to

    Text Solution

    |

  6. If the graph of the function y = f(x) is symmetrical about the line x ...

    Text Solution

    |

  7. If the sides of a triangle are in the ratio 1 : sqrt3 : 2, then the an...

    Text Solution

    |

  8. Let f(x) be a strictly increasing and differentiable function, then li...

    Text Solution

    |

  9. If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which ...

    Text Solution

    |

  10. Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2]. If f(x) is ...

    Text Solution

    |

  11. Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k, then

    Text Solution

    |

  12. The area enclosed between the curves y=ax^2 and x=ay^2(a > 0) is 1 sq....

    Text Solution

    |

  13. lim(nrarroo) sum(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

    Text Solution

    |

  14. The angle between the tangents drawn from the point (1,4) to the par...

    Text Solution

    |

  15. A variable circle passes through the fixed point A(p,q) and touches t...

    Text Solution

    |

  16. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

    Text Solution

    |

  17. A line line makes the same angle theta with each of the x and z-axes....

    Text Solution

    |

  18. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

    Text Solution

    |

  19. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

    Text Solution

    |

  20. Let v=2 vec i+vec j-vec k, w=vec i+ 3 vec k and vec u is a unit vector...

    Text Solution

    |