Home
Class 12
MATHS
Let S be the set of all triangles and R^...

Let `S` be the set of all triangles and `R^+` be the set of positive real numbers. Then the function `f: SrarrR^+,f(Delta)=area of Delta ,where Delta in S ,` is injective but not surjective. surjective but not injective injective as well as surjective neither injective nor surjective

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

Let A be the set of triangles in a plane and RR^(+) be the set of positive real numbers. Then show that, the function f:A rarr RR^(+) defined by , f(x)= area of triangle x, is many -one and onto.

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) non of these

Let A be the set of quadrilaterals in a plane and RR^(+) be the set of positive real numbers. Prove that, the function f: A rarr RR ^(+) defined by f(x) = area of quadrilateral x, is * many-one and onto.

Let NN be the set of natural numbers and D be the set of odd natural numbers. Then show that the mapping f:NN rarr D , defined by f(x)=2x-1, for all x in NN is a surjection.

Let R be the set of real numbers. Define the real function f: R to R by f(x)=x+10 and sketch the graph of this function.

Let f:[-oo,0)->(1,oo) be defined as f(x)=(1+sqrt(-x))-(sqrt(-x)-x) then f(x) is (A) injective but not surjective (B) injective as well as surjective (C) neither injective nor surjective (D) surjective nut not injective

Let f:R rarr R defined by f(x)= x^2/(1+x^2) . Prove that f is neither injective nor surjective.

Let CC and RR be the sets of complex numbers and real numbers respectively . Show that, the mapping f:CC rarr RR defined by, f(z)=|z| , for all z in CC is niether injective nor surjective.

Show that f: R->R defined by f(x)=(x-1)(x-2)(x-3) is surjective but not injective.

Let p,q,r be the altitudes of a triangle with area s and perimeter 2t. Then the value of 1/p+1/q+1/r is

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let f(x) be periodic and k be a positive real number such that f(x+k)+...

    Text Solution

    |

  2. Find the domain of the following functions: f(x)=(x-3)/((x+3)sqrt(x^2-...

    Text Solution

    |

  3. Let S be the set of all triangles and R^+ be the set of positive real ...

    Text Solution

    |

  4. Check whether the function defined by f(x+lambda)=1+sqrt(2f(x)-f^2(x))...

    Text Solution

    |

  5. Solve (x-1)^2(x+4)<0

    Text Solution

    |

  6. If f(x)={x ,x is rational 1-x ,x is irrational ,then f(f(x)) is

    Text Solution

    |

  7. An odd function is symmetric about the vertical line x=a ,(a >0),a n d...

    Text Solution

    |

  8. Solve x >sqrt((1-x))

    Text Solution

    |

  9. The range of f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2) is {0,1+pi/2} ...

    Text Solution

    |

  10. If f(x)=lambda|sinx|+lambda^2|cosx|+g(lambda) has a period = pi/2 then...

    Text Solution

    |

  11. Find domain of f(x) = sqrt(1 - sqrt(1-sqrt(1 - x^2))).

    Text Solution

    |

  12. If f(x) =ln ((x^2 + e)/(x^2 + 1)), then range of f(x) is

    Text Solution

    |

  13. If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for allx , th...

    Text Solution

    |

  14. Solve (x-1)|x+1|cosx>0,forx in [-pi,pi]

    Text Solution

    |

  15. The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the great...

    Text Solution

    |

  16. Solve (2x+1)(x-3)(x+7)<0

    Text Solution

    |

  17. Which of the following pair(s) of function have same graphs? f(x)=(s...

    Text Solution

    |

  18. If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

  19. Solve 2/x<3

    Text Solution

    |

  20. The domain of the function f(x)=1/(sqrt(4x-|x^2-10 x+9|)) is

    Text Solution

    |