Home
Class 11
MATHS
Given the function f (x) =(a ^(x) + a ^(...

Given the function `f (x) =(a ^(x) + a ^(-x))/(2), a gt 2,` then `f (x+y) + f(x -y) =`

A

`2f (x). F (y)`

B

`f (x). F(y)`

C

`(f(x))/(f (y))`

D

`1/2 f (x) f (y)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos
  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos
  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

Given the function f(x)=(a^(x)+a^(-x))/(2)(wherea>2)dot Then f(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) (f(x))/(f(y)) (D) none of these

Given the function f(x)=(a^(x)+a^(-x))/(2)(a>0) If f(x+y)+f(x-y)=kf(x)*f(y) then k has the value equal to

If f(x)=(2^(x)+2^(-x))/(2) , then f(x+y).f(x-y) is equal to

If f(x)=(a^(x)+a^(-x))/(2) and f(x+y)+f(x-y)=kf(x)f(y) then k=

If the function f:R rarr R defined by f(x)=(3^(x)+3^(-x)) , then show that f(x+y) = f(x-y) = 2f(x)f(y) .

Let f (x) = a ^ x ( a gt 0 ) be written as f ( x ) = f _ 1 (x ) + f _ 2 (x) , where f _ 1 ( x ) is an even function and f _ 2 (x) is an odd function. Then f _ 1 ( x + y ) + f _ 1 ( x - y ) equals :

" If the function "f:R rarr R" defined by "f(x)=(3^(x)+3^(-x))/(2)," then show that "f(x+y)+f(x-y)=2f(x)f(y)"

A function y=f(x) satisfying f'(x)=x^(-(3)/(2)),f'(4)=2 and f(0)=0 is

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. If f(x) = cos (log (e) x), then f (x) f(y) -1/2 [f(xy) +f((x)/(y))] ha...

    Text Solution

    |

  2. The values of ba n dc for which the identity of f(x+1)-f(x)=8x+3 is sa...

    Text Solution

    |

  3. Given the function f (x) =(a ^(x) + a ^(-x))/(2), a gt 2, then f (x+y)...

    Text Solution

    |

  4. If f(x) = log ((1+x)/(1-x)), then f((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  5. If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(...

    Text Solution

    |

  6. If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest...

    Text Solution

    |

  7. Prove that if f (x) is periodic function with period T, then the funct...

    Text Solution

    |

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

    Text Solution

    |

  9. Let f {(1,1), (2,4), (0,-2), (-1,-5)} be a linear function from Z into...

    Text Solution

    |

  10. If f (x) =log ""(1+x)/(1-x) then-

    Text Solution

    |

  11. The real valued function f(x)=(a^x-1)/(x^n(a^x+1)) is even, then the v...

    Text Solution

    |

  12. The function f(x) = sec[log(x + sqrt(1+x^2))] is

    Text Solution

    |

  13. The function f(x)= sin | log (x+ sqrt(x^(2) +1)) | is-

    Text Solution

    |

  14. If f(x)+2f((1)/(x))=3x, x ne 0 and S={x in R: f(x) = f(-x)}, " then ...

    Text Solution

    |

  15. If [x] denotes the greatest integer le x, then [(2)/(3)]+[(2)/(3)+(1)/...

    Text Solution

    |

  16. f(x)=cos^(2)x+cos^(2)(pi/3+x)-cosx*cos(x+pi/3) is

    Text Solution

    |

  17. If y=f(x)=((x+2))/((x-1)),t h e n x=f(y) (b) f(1)=3 y increases wit...

    Text Solution

    |

  18. If g (y) is inverse of function f :R to R given by f (x)=x+3, then g (...

    Text Solution

    |

  19. If f:R to R is defined by f(x)=|x|, then

    Text Solution

    |

  20. If f(x)=3x-5, then f^(-1)(x) is given by 1/((3x-5)) is given by ((x+...

    Text Solution

    |