Home
Class 12
MATHS
If f(x+ay,x -ay) = axy then f(x,y) = .....

If `f(x+ay,x -ay) = axy ` then f(x,y) = ......

A

xy

B

`x^2-a^(2)y^2`

C

`(x^(2)-y^2)/4`

D

`(x^(2)-y^2)/a^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice Work|54 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|19 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Practice Work|66 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

If f(x+2y , x-2y)=x y , then f(x,y) equals

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

f:R rarr R, function f(x) is defined as f(x)= 2x +|x| then f(2x)+f(-x)-f(x) = ...........

If f(x)= (x-3)/(x + 1) then f[f {f(x)}] = …….

f(x) is a continuous and differentiable function. f'(x) ne 0 and |{:(f'(x),f(x)),(f''(x),f'(x)):}|=0 . If f(0)=1 and f'(0)=2 then f(x)=....

A function y = f(x) satisfies the condition f(x+(1)/x) =x^(2)+1/(x^2)(x ne 0) then f(x) = ........

f(x+ y) = f(x) f(y) , For AA x and y . If f(3)= 3 and f'(0) =11 then f'(3)= …….

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.

Let f be a function such that f(x+f(y)) = f(x) + y, AA x, y in R , then find f(0). If it is given that there exists a positive real delta such that f(h) = h for 0 lt h lt delta , then find f'(x)

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook based MCQs
  1. If f(1) = 1, f(n+1)= 2f (n) + 1, n ge 1 then f(n) = .........

    Text Solution

    |

  2. A function y = f(x) satisfies the condition f(x+(1)/x) =x^(2)+1/(x^2)(...

    Text Solution

    |

  3. If f(x+ay,x -ay) = axy then f(x,y) = ......

    Text Solution

    |

  4. For function f(x) = (alpha x)/(x+1) , x ne -1 if fof(x) = x then alph...

    Text Solution

    |

  5. For real valued functions f and g, f(x) = 2sin (pi/x) and g(x) = sqrtx...

    Text Solution

    |

  6. The domain of the real value function f(x) = sqrt(5-4x-x^(2))+x^(2)log...

    Text Solution

    |

  7. The domian of sin^(-1)[log(3)(x/3)] is .......

    Text Solution

    |

  8. Range of the function f(x)= (x^(2) + x + 2)/(x^(2) + x + 1) is……

    Text Solution

    |

  9. If g(x) =x^(2)+x-2 and 1/(2) (gof) (x) =2x^(2)-5x+2 then f(X) =..........

    Text Solution

    |

  10. g(x) = 1 + sqrt(x) and f(g(x)) =3 +2sqrtx+x then f(x) = ......

    Text Solution

    |

  11. If real function f(x) =(x+1)^(2) and g(x) =x^(2) +1 then (fog) (-3) = ...

    Text Solution

    |

  12. f(x) = cot^(-1)x: R^(+) rarr (0,pi) and g(x) = 2x-x^(2): R rarrR then ...

    Text Solution

    |

  13. The domian of f is [-5,7] and g(x) = |2x+5| then the domian of (fog) (...

    Text Solution

    |

  14. A set A has 3 elements and a set B has 4 elements . The number of one...

    Text Solution

    |

  15. f: R rarr R , f(x) = (x-1) (x-2)(x-3) then f is ........

    Text Solution

    |

  16. f: N rarr N , f(n) = (n+5)^(2) , n in N , then the function f is ........

    Text Solution

    |

  17. f: [0,oo) rarr [0,oo) , f(x) = x/(1+x) then the function f is ...........

    Text Solution

    |

  18. f(x) =x^3/3+x^2/2+ax +b,AAx inR. If (x) is one one function then the m...

    Text Solution

    |

  19. f(x) = x^(2) - 2x -1, AA x in R, f:(-oo,oo] rarr [b,oo) is one one an...

    Text Solution

    |

  20. f(x) = (e^(x)-e^(-x))/(e^(x)+e^(-x))+2 . The inverse of f(x) is .........

    Text Solution

    |