Home
Class 12
MATHS
Show that if f1a n df2 are one-one map...

Show that if `f_1a n df_2` are one-one maps from `RtoR ,` then the product `f_1×f_2: RtoR` defined by `(f_1×f_2)(x)=f_1(x)f_2(x)` need not be one-one.

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Show that if f_1a n df_1 are one-one maps from RtoR , then the product f_1xf_2: RvecR defined by (f_1xf_2)(x)=f_1(x)f_2(x) need not be one-one.

Show that if f_1 and f_2 are one-one maps from R to R , then the product f_1xxf_2: R->R defined by (f_1xxf_2)(x)=f_1(x)f_2(x) need not be one-one.

Give examples of two one-one functions f_1 and f_2 from R to R such that f_1+f_2: R->R , defined by (f_1+f_2)(x)=f_1(x)+f_2(x) is not one-one.

The function f:RtoR defined by f(x)=e^(x) is

If f:RtoR is defined by f(x)=ax+b,ane0 then f^(-1)(x)

Suppose f_1a n df_2 are non-zero one-one functions from RtoRdot is (f_1)/(f_2) necessarily one-one? Justify your answer. Here, (f_1)/(f_2): RtoR is given by ((f_1)/(f_2))(x)=(f_1(x))/(f_2(x)) for all x∊Rdot

If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

If a function f: R to R is defined as f(x)=x^(3)+1 , then prove that f is one-one onto.

Suppose f_1a n df_2 are non=zero one-one functions from RtoRdot is (f_1)/(f_2) necessarily one-one? Justify your answer. Here, (f_1)/(f_2): RvecR is given by ((f_1)/(f_2))(x)=(f_1(x))/(f_2(x)) for all xRdot

Prove that the function f:N to N , defined by f(x)=x^(2)+x+1 is one-one but not onto.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Find gofa n dfog wehn f: RvecR and g: RvecR are defined by f(x)=2x+...

    Text Solution

    |

  2. Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(...

    Text Solution

    |

  3. Show that if f1a n df2 are one-one maps from RtoR , then the produ...

    Text Solution

    |

  4. Give examples of two surjective function f1 and f2 from Z to Z such...

    Text Solution

    |

  5. Given examples of two one-one functions f1a n df2 from R to R such ...

    Text Solution

    |

  6. If f: A->B and g: B->C are onto functions show that gof is ...

    Text Solution

    |

  7. Show that the logarithmic function f: R0+vecR given by f(x)=(log)a ...

    Text Solution

    |

  8. If f: AvecBa n dg: BvecC are one-one functions, show that gof is on...

    Text Solution

    |

  9. If f: R->R be the function defined by f(x)=4x^3+7, show that f is a ...

    Text Solution

    |

  10. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |

  11. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor on...

    Text Solution

    |

  12. Suppose f1a n df2 are non-zero one-one functions from RtoRdot is (f1...

    Text Solution

    |

  13. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g ={(1,\ 3),\ (3,\ 3),\ (4,\...

    Text Solution

    |

  14. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

    Text Solution

    |

  15. Let f: RvecR and g: RvecR be defined by f(x)=x^2 and g(x)=x+1. Show ...

    Text Solution

    |

  16. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

    Text Solution

    |

  17. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  18. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

    Text Solution

    |

  19. Show that the exponential function f: R to R , given by f(x)=e^x , i...

    Text Solution

    |

  20. Let A="{"-1,0,1")"a n df={(x , x^2): xA}dot Show that f: AvecA is neit...

    Text Solution

    |