Home
Class 12
MATHS
Find whether the following functions ...

Find whether the following functions are one-one or not: `f: Rvecgi v e nb yf(x)=x^3+2fora l lx in Rdot` `f: ZvecZgi v e nb yf(x)=x^2+1fora l lx in Zdot`

Text Solution

AI Generated Solution

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

Find whether the following functions are one-one or not. f:ZtoZ , defined by f(x)=x^(2)+5 for all x inZ

Find whether the following functions are one-one or not. f:RtoR , defined by f(x)=x^(3),x inR

Find whether the following functions are one-one or many-one f(x)=sqrt(1-e^(1/x-1))

Find whether the following are into functions (surjections) or not. f:RtoR defined by f(x)=x^(2)+3 for all x inR

Examine whether the following functions are one-one, many-one or into, onto f(x)=x^(2)+lnx

Find whether the following function is differentiable at x = 1 and x = 2 or not : f(x)={x ,x 2

Find whether the following function are one-one or many -one & into or onto if f:DtoR where D is its domain f(x)=x cos x

Find whether the following function is differentiable at x = 1 and x = 2 or not: f(x)={x ;x 2

Discuss the surjectivity of the following functions: f: R-> given by f(x)=x^3+2 for all x in Rdot

Find whether the following function are one-one or many -one & into or onto if f:DtoR where D is its domain f(x)=1/(sinsqrt(|x|))

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If the function fa n dg are given by f={(1,2),(3,5),(4,1)}a n dg="("(2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If f:[0,oo)vecRa n dg: RvecR be defined as f(x)=sqrt(x) and g(x)=-x^2-...

    Text Solution

    |

  17. Let f and g be real functions defined by f(x)=x/(x+1) a n d g(x)=1/(x...

    Text Solution

    |

  18. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

    Text Solution

    |

  19. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

    Text Solution

    |

  20. If f: Rvec is defined by f(x)=2x+7. Prove that f is a bijection. Also,...

    Text Solution

    |