Home
Class 12
MATHS
Let f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2...

Let `f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2))[f(x)` is not identically zero]. Then `a) f(4x^3-3x)+3f(x)=0` `b) f(4x^3-3x)=3f(x)` `c) f(2xsqrt(1-x^2)+2f(x)=0` `d) f(2xsqrt(1-x^2)=2f(x)`

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

f(x)=sin^(-1)(2xsqrt(1-x^2)) then f'(x)=

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these

If f(x) = xsqrt (x^2+a^2) +a^2 log(xsqrt(x^2+a^2)) then find the value of f(0).

If y = f(x^2) and f'(x) = sqrt (3x^2+1) , find [(dy)/(dx)]_(x=2)

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

IF y=f(x^(2)) and f'(x)=sqrt(3x^(2)+1) , find [(dy)/(dx)]_(x=2) .

2f(x)+3f(-x)=15-4x then [f(1)+f(-1)]=?

If f(x)=x^3-x^2+100x+2002 ,t h e n a) f(1000)>f(1001) b) f(1/(2000))>f(1/(2001)) c) f(x-1)>f(x-2) d) f(2x-3)>f(2x)

If f(x)=2^x the f(x+3)/ f(x-1) =?

If 2f((1)/(x))+f(x)=3x , find f(x-(1)/(x))

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let E={1,2,3,4},F={1,2} then the number of onto functions from E to F ...

    Text Solution

    |

  2. f(x) = (alpha x)/(x + 1) (x ne -1), then for what value of alpha , f{f...

    Text Solution

    |

  3. Let f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2))[f(x) is not identically zer...

    Text Solution

    |

  4. Consider the real-valued function satisfying 2f(sinx)+f(cosx)=xdot th...

    Text Solution

    |

  5. If the function f satisfies the relation f(x+y)+f(x-y)=2f(x)xxf(y), AA...

    Text Solution

    |

  6. If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,...

    Text Solution

    |

  7. Which of the following functions are identical? (a)f(x)=1nx^2a n dg(x...

    Text Solution

    |

  8. Which of the following functions have the graph symmetrical about the ...

    Text Solution

    |

  9. The range of given function f(x)=^(7-x)P(x-3) is given by

    Text Solution

    |

  10. Let f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi] and g(x)=max{1,|x-1|} x in R...

    Text Solution

    |

  11. If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in R an...

    Text Solution

    |

  12. Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",", x ge 3):} and g(x)={(x-3"...

    Text Solution

    |

  13. Let f(x)=(3)/(4)x+1,f^(n)(x) be defined as f^(2)(x)=f(f(x)), and for n...

    Text Solution

    |

  14. If f:{1,2,3....}->{0,+-1,+-2...} is defined by f(n)={n/2, if n is ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |