Home
Class 12
MATHS
Find the natural no. a for which sum (k=...

Find the natural no. a for which `sum _(k=1)^nf(a+k)=16(2^n-1)` where the function f satisfies f(x+y)=f(x)f(y) for all natural no. x,y, and further f(1)=2.

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the natural number a for which sum_(k=1)^nf(a+k)=16(2^n-1) where the function f satisifies f(x+y)=f(x)f(y) for x, y in N and f(1)=2.

Find the natural number a for which sum_(k=1) ^(n)f(a+k)= 16(2^(n)-1) where the function f satisfies the relation f(x+y)=f(x)f(y) for all natural numbers x,y and further f(1)=2 .

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

If f : R to R satisfies f(x + y)=f(x)+f(y) for all x, y in R and f(1)=7 , then sum_(r=1)^n f(r)

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

f(x) is real valued function, satisfying f(x+y)+f(x-y)=2f(X),f(y) for all y ne R , then

A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

If the function f satisfies the reation f(x+y)+f(x-y)=2f(x) f(y) Aax,yin RR and f(0) ne 0 then ____

If the function f satisfies the relation f(x+y)+f(x-y)=2f(x)xxf(y), AA x, y, in R and f(0) ne 0 , then

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If f(x)=(1−x)^(1/2) and g(x)=ln(x) then the domain of (gof)(x) is

    Text Solution

    |

  2. Find the domain of the function: f(x)=sin^(-1)(|x-1|-2)

    Text Solution

    |

  3. Find the natural no. a for which sum (k=1)^nf(a+k)=16(2^n-1) where the...

    Text Solution

    |

  4. Let f(x)=tanx a n d g(f(x))=f(x-pi/4), where f(x)a n dg(x) are real ...

    Text Solution

    |

  5. Find the range of f(x)=tan^(-1)sqrt((x^2-2x+2))

    Text Solution

    |

  6. The domain of f(x) is (0,1) Then the domain of (f(e^x)+f(1n|x|) is (...

    Text Solution

    |

  7. If f(x)=3x-2a n d(gof)^(-1)(x)=x-2, then find the function g(x)dot

    Text Solution

    |

  8. Find the range of f(x)=sqrt(cos^(-1)sqrt((1-x^2))-sin^(-1)x)

    Text Solution

    |

  9. The domain of f(x)=1/(sqrt(|cosx|+cosx)) is

    Text Solution

    |

  10. If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x)...

    Text Solution

    |

  11. Find the domain of the function: f(x)=cos^(-1)((6-3x)/4)+cos e c^(-1)(...

    Text Solution

    |

  12. If f(2x+3y, 2x-7y)=20x, then f(x,y) equals :

    Text Solution

    |

  13. Solve the equation x^2-x+1=1/2+sqrt(x-3/4), w h e r e xgeq3/4

    Text Solution

    |

  14. Find the domain of the function: f(x)=sqrt(sec^(-1)((2-|x|)/4))

    Text Solution

    |

  15. Let X={a1, a2,.. ,a6}a n dY={b1, b2,b3}dot The number of functions f f...

    Text Solution

    |

  16. Find the inverse of f(x)={(x ,, x<1),(x^2 ,, 1lt=xlt=4), (8sqrt(x) ,,...

    Text Solution

    |

  17. Write the equivalent definition and draw the graphs of the following ...

    Text Solution

    |

  18. The range of f(x)=[sinx+[cosx+[tanx+[secx]]]],x in (0,pi/4),w h e r e ...

    Text Solution

    |

  19. Which of the following functions has inverse function?

    Text Solution

    |

  20. Find the range of f(x)=cos^(-1)((sqrt(1+2x^2))/(1+x^2))

    Text Solution

    |