Home
Class 12
MATHS
Prove that f(x)=root(3)(1-(x)^2+root(3)(...

Prove that `f(x)=root(3)(1-(x)^2`+`root(3)(1+(x)^2)` is an even function

Promotional Banner

Topper's Solved these Questions

  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

  • Equations, Inequation and Expressions

    A DAS GUPTA|Exercise Exercise|301 Videos

  • Heights and Distances

    A DAS GUPTA|Exercise Exercise|3 Videos

Similar Questions

Explore conceptually related problems

root(3)(x^(2))+root(3)(x^(2))=3

If f(x)=root(3)((1-x^(2)))+root(3)((1+x^(2))) , then f(x) is :

Prove that the real valued function f(x)=(x)/(e^(x)-1)+(x)/(2)+1 is an even function on R-{0}

If function f(x) = (sqrt(1+x) - root(3)(1+x))/(x) is continuous function at x = 0, then f(0) is equal to

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

Solve : root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2)) .

[" The derivative of the function "],[f(x)=root(3)((x^(2)-1)^(2))],[" does not exist for "x=+-1],[" does not exist for "x=2/3],[" exists for all "x],[" does not exist for "x=3/2]

lim_(x rarr0)(root(3)(1+x^(2))-root(4)(1-2x))/(x+x^(2)) is equal to

Find the value of f(1) so that the function f(x)=((root(3)x^2-(2x^(1//3)-1)))/(4(x-1)^2), x ne 1 is continuous at x=1.

A DAS GUPTA-Function-Exercise
  1. Let f : {x,y, z} to {a, b, c} be a one-one function. If it is known th...

    Text Solution

    |

  2. Prove that the product of two odd functions is an even function while ...

    Text Solution

    |

  3. Prove that f(x)=root(3)(1-(x)^2+root(3)(1+(x)^2) is an even function

    Text Solution

    |

  4. Extend f(x)=x^2+x defined in [0,3] onto the interval[-3,3] so that f(x...

    Text Solution

    |

  5. Period of |sinx+cosx| is

    Text Solution

    |

  6. If f(x) in [1,2] where x in R and for a fixed positive real number p, ...

    Text Solution

    |

  7. Let f (x ) and g(x) be increasing and decreasing functions respectivel...

    Text Solution

    |

  8. Computer the inverse of the function : f(x) = (x + sqrt(x^(2) + 1))

    Text Solution

    |

  9. If f(x)=1-x/(1+x), x not equal to -1 then f{f(1/x)}=

    Text Solution

    |

  10. If f(x)=cos(logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

    Text Solution

    |

  11. If f(x)=(x+1)/x and phi(x)=(x^4+1)/(x^4) then phi(a)=-- where f(a)=5.

    Text Solution

    |

  12. If f(x) is a polynomial function of the second degree such tha f(0)=5,...

    Text Solution

    |

  13. If f(x+1)=x^(2)-3x+2 then f(x) is equal to

    Text Solution

    |

  14. If f is an even function defined on the interval (-5,5), then four rea...

    Text Solution

    |

  15. If f(x) is a periodic function of the period k then f(ax+b) is a perio...

    Text Solution

    |

  16. The value of f(x)=3sin((pi^2)/(16)-x^2) lie in the interval

    Text Solution

    |

  17. If f:RrarrR be a function given f(x)=sqrt1- sqrt(1-x^2) then the domai...

    Text Solution

    |

  18. If the function f : [2,+prop)rarrX be bijective wheras f(x)= 5-4x+x^2 ...

    Text Solution

    |

  19. Find the domain f(x)=log(100x)((2 log(10) x+1)/-x)

    Text Solution

    |

  20. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

    Text Solution

    |