Home
Class 11
MATHS
If the function f: R to R defined by f(...

If the function `f: R to R ` defined by `f(x)=(3^(x)+3^(-x))/(2)`, then S.T `f(x+y)+f(x-y)=2f(x)f(y)`.

Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE -1.2 (VERY SHORT ANSWER TYPE QUESTIONS)|2 Videos

  • FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE -1.2 (SHORT ANSWER TYPE QUESTIONS)|7 Videos

  • FUNCTIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|50 Videos

  • ERRORS AND APPROXIMATIONS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTION|15 Videos

  • HEIGHTS AND DISTANCES

    AAKASH SERIES|Exercise PRACTICE SHEET Exercise-I (Level-II) (Straight Objective Type Questions)|13 Videos

Similar Questions

Explore conceptually related problems

If f: R to R is defined by f(x)=(x^(2)-4)/(x^(2)+1) , then f(x) is

If f: R to R is defined by: f(x-1) =x^(2) + 3x+2 , then f(x-2) =

If f: R to R defined by f(x) =x^(2)-2x-3 , then f is:

If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3) , then S.T f(x) + f(1//x) = 0 .

If f : R to R is defined by f(x) = x^(2)- 6x + 4 then , f(3x + 4) =

If f: R to R is defined by f(x) = 2x+|x| , then show that f(3x) -f(-x) -4x=2f(x) .

Let the function f: R to R be defined by f(x) = 2x + sinx for x in R , then f is

If f:[0,infty) to R defined by f(x) = x^(2) , then f is

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

If f:R rarrR is defined by f(x)=x^(2)+3x+2, then f(x-1)=

AAKASH SERIES-FUNCTIONS -EXERCISE -1.1 (VERY SHORT ANSWER QUESTIONS)
  1. Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,3,4}. to B={1...

    Text Solution

    |

  2. If f= {(1, 2), (2, -3), (3, -1)} then find: (i) 2f, (ii) 2+f, (iii) ...

    Text Solution

    |

  3. If f={(4,5),(5,6), (6,-4)} and g={(4,-4),(6,5),(8,5)} then find: (i)...

    Text Solution

    |

  4. If f(x) = x^(2) and g(x) = Ixl then find the values of: (i) f+g, (i...

    Text Solution

    |

  5. If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3), then S.T f(x) +...

    Text Solution

    |

  6. f:R-{0} to R is defined as f(x)=x+1/x then show that (f(x))^(2)=f(x^(2...

    Text Solution

    |

  7. If f:R-(pm1)toR is defined by f(x)=log|(1+x)/(1-x)|, then show that f(...

    Text Solution

    |

  8. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

    Text Solution

    |

  9. If the function f: R to R defined by f(x)=(4^(x))/(4^(x)+2), then show...

    Text Solution

    |

  10. If the function f: R to R defined by f(x)=(3^(x)+3^(-x))/(2), then S....

    Text Solution

    |

  11. If f: R to R, g : R to R are defined by f(x) = 4x-1 and g(x) = x^(2)+2...

    Text Solution

    |

  12. If f: R to R, g : R to R are defined by f(x) =3x-1, g(x) =x^(2)+1, the...

    Text Solution

    |

  13. If f(x)=(x)/(sqrt(1-x^(2))), g(x)=(x)/(sqrt(1+x^(2))) then (fog)(x)=

    Text Solution

    |

  14. If f(x) = 1//x, g(x) = sqrt(x) for all x in (0,oo), then find (gof)(x)...

    Text Solution

    |

  15. If f(x) = 2, g(x) = x^(2), h(x) = 2x then find (fogoh)(x)

    Text Solution

    |

  16. If f(x) = (x+1)/(x-1) (x ne -1) then find (fofof)(x) and (fofofof)(x).

    Text Solution

    |

  17. Let f(x) = x^(2), g(x) = 2^(x). Then solve the equation (fog)(x)=(gof)...

    Text Solution

    |

  18. Determine whether the following functions are even or (odd). (i) f(x...

    Text Solution

    |

  19. P.T the real valued function f(x)= (x)/(e^(x)-1) + x/2 + 1 is an even ...

    Text Solution

    |

  20. If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, f...

    Text Solution

    |