Home
Class 12
MATHS
If p and q are positive integers, f is a...

If p and q are positive integers, f is a function defined for positive number and attain only positive value such that `f(xf(y)) = x^p y^q`, prove that `q = p^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

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

Prove that q^^~p -=~ (q to p)

If p and q are positive, then prove that the coefficients of x^p and x^q in the expansion of (1+x)^(p+q) will be equal.

Prove that ~(~pto ~q) -=~p ^^q

If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r^2t^4s^2 , then find the number of ordered pair (p,q).

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

Let A={x in R:x" is not a positive integer "} define a function f:AtoR" such that "f(x)=(2x)/(x-1) . Then f is

If f(x) = (p - x^n)^(1/n), p gt 0 and n is positive integer, then the value of f[f(x)]

If y=f(x) =(px+q)/(rx-p), show that x = f(y).

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If f:{1,2,3....}->{0,+-1,+-2...} is defined by f(n)={n/2, if n is ...

    Text Solution

    |

  2. If f: Rrarr[0,oo)is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), th...

    Text Solution

    |

  3. If p and q are positive integers, f is a function defined for positive...

    Text Solution

    |

  4. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  5. Show that any function can be expressed as the sum of an odd function ...

    Text Solution

    |

  6. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  7. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  8. Let f(x)=log2 log3log4log5(sin x+a^2). Find the set of values of a for...

    Text Solution

    |

  9. Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2...

    Text Solution

    |

  10. If fa n dg are two distinct linear functions defined on R such that th...

    Text Solution

    |

  11. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that ...

    Text Solution

    |

  12. Let f:XtoY be a function defined by f(x)=asin(x+pi/4)+bcosx+c. If f is...

    Text Solution

    |

  13. If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx ...

    Text Solution

    |

  14. Let R="{"x , y")": x , y in R ,x^2+y^2lt=25}andR^(prime)={(x , y): x ...

    Text Solution

    |

  15. A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c le...

    Text Solution

    |

  16. The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes...

    Text Solution

    |

  17. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetric ab...

    Text Solution

    |

  18. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fr...

    Text Solution

    |

  19. Let f: RvecR be a continuous and differentiable function such that (f(...

    Text Solution

    |

  20. The possible values of a such that the equation x^2+2a x+a=sqrt(a^2+x-...

    Text Solution

    |