Home
Class 12
MATHS
Give examples of two one-one function...

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.

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_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.

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.

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.

The function f : R -> R is defined by f (x) = (x-1) (x-2) (x-3) is

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

The function f:R→R defined by f(x)=(x−1)(x−2)(x−3) is

Prove that the function f : R ->R , given by f (x) = 2x , is one-one and onto.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A=R-[2] \ a n d \ B=R-[1]. If f: A->B is a mapping defined by f(x)...

    Text Solution

    |

  2. Show that if f1a n df1 are one-one maps from RtoR , then the pro...

    Text Solution

    |

  3. Give examples of two one-one functions f1 and f2 from R to R such t...

    Text Solution

    |

  4. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

    Text Solution

    |

  5. If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given ...

    Text Solution

    |

  6. If the function fa n dg are given by f={(1,2),(3,5),(4,1)}a n dg="("(2...

    Text Solution

    |

  7. Suppose f1a n df2 are non=zero one-one functions from RtoRdot is (f...

    Text Solution

    |

  8. Find whether the following functions are one-one or not: f: Rvecgi...

    Text Solution

    |

  9. If the function f and g are given by f={(1,2),(3,5),(4,1)} and g={(2,...

    Text Solution

    |

  10. Discuss the surjectivity of the following functions: f: R-> given by ...

    Text Solution

    |

  11. Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z ...

    Text Solution

    |

  12. Let A be the set of all 50 students of class XII in a central school. ...

    Text Solution

    |

  13. Show that the function f: RvecR defined by f(x)=3x^3+5 for all x in R...

    Text Solution

    |

  14. Show that the function f: RvecR given by f(x)=cosxfora l lx in R , is...

    Text Solution

    |

  15. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

    Text Solution

    |

  16. If f(x) = x/(sqrt(1+x^2) then fofof(x)

    Text Solution

    |

  17. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

    Text Solution

    |

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

    Text Solution

    |

  19. Let f: R-R be a function given by f(x)=a x+b for all x in R . Find th...

    Text Solution

    |

  20. If f(x)=e^x and g(x)=(log)e x(x >0), find foga n dgofdot Is fog=gof?

    Text Solution

    |