Home
Class 12
MATHS
If f(2x+y/8,2x-y/8)=x y , then f(m , n)+...

If `f(2x+y/8,2x-y/8)=x y` , then `f(m , n)+f(n,m)=0` (a) only when `m=n` (b) only when `m!=n` (c) only when `m=-n` (d) for all m and n

A

only when `m = n`

B

only when `m ne n`

C

only when `m = -n`

D

for all m and n

Text Solution

Verified by Experts

The correct Answer is:
D
Let `2x+(y)/(8)=alpha" and " 2x-(y)/(8)=beta.`
Then ` x=(alpha+beta)/(4) and y=4(alpha-beta).`
Given `f(2x+(y)/(8), 2x-(y)/(8))=xy`
` :. f(alpha, beta)=alpha^(2)-beta^(2)`
`or f(m,n)+f(n,m)=m^(2)-n^(2)+n^(2)-m^(2)=0` for all m,n
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 f (2x+3) =sin x+2^(x), then the value of f (4m-2n+3) is-

If f(2x+3)=sinx+2^(x) , then the value of f(4m-2n+3) is -

If f(x)= (x^m)^(1/n) ,n in N , is an even function, then m is (a)even integer (b) odd integer (c) any integer (d) f(x)-e v e ni s not pos s i b l e

If (x+y)^(m+n)=x^(m)y^(n) , then the value of (dy)/(dx) is -

If y=f(x)=(3x-5)/(2x-m)and f(y)=x, find the value of m.

If f(x+y)=f(x)+f(y)-x y-1AAx , y in R and f(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in R and f(1)=5,t h e n (a) f(x) is an odd function (b) f(x) is an even function (c) sum_(r=1)^mf(r)=5^(m+1)C_2 (d) sum_(r=1)^mf(r)=(5m(m+2))/3

Let h(x)=x^(m/n) for x in R , where m and n are odd numbers where 0 < m < n. Then y= h(x) has a. no local extremums b. one local maximum c. one local minimum d. none of these

If m = sqrtfrac(n)(n+1/2) and m = 1/2, then n =

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^...

    Text Solution

    |

  2. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

    Text Solution

    |

  3. If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (...

    Text Solution

    |

  4. Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...

    Text Solution

    |

  5. If f(x+y)=f(x)+f(y)-x y-1AAx , y in R and f(1)=1, then the number of ...

    Text Solution

    |

  6. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x-1)...

    Text Solution

    |

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

    Text Solution

    |

  8. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

    Text Solution

    |

  9. If f(x+1)+f(x-1)=2f(x) and f(0)=0, then find f(n),n in N , is

    Text Solution

    |

  10. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

    Text Solution

    |

  11. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

    Text Solution

    |

  12. If f(3x+2)+f(3x+29)=0x in R , then the period of f(x) is (a) 7 (b) 8 ...

    Text Solution

    |

  13. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...

    Text Solution

    |

  14. Find f(x) when it is given by f(x)=max{x^(3),x^(2),(1)/(64)},AA x in...

    Text Solution

    |

  15. The equation ||x-2|+a|=4 can have four distinct real solutions for x i...

    Text Solution

    |

  16. Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...

    Text Solution

    |

  17. If f(x) is a real=valued function defined as f(x)=1N(1-sinx), then the...

    Text Solution

    |

  18. Let f(x)=x+2|x+1|+x-1|dotIff(x)=k has exactly one real solution, then ...

    Text Solution

    |

  19. The number of solutions of 2cosx=|sinx|,0lt=xlt=4pi, is (a) 0 (b) 2 ...

    Text Solution

    |

  20. Given that f(x)=5x^2−8x,g(x)=x^2−5x−24 . Find ( f/g)(x)

    Text Solution

    |