Home
Class 12
MATHS
Show that the function f: RvecR given by...

Show that the function `f: RvecR` given by `f(x)=cosxfora l lx in R ,` is neither one-one nor onto

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

Show that the function f: R->R given by f(x)=cosx for all x in R , is neither one-one nor onto.

Show that the function f:R->R defined by f(x)=x/(x^2+1) AA x in R is neither one-one nor onto. Also if g:R->R is defined by g(x)=2x-1 find fog(x)

Show that the Modulus Function f : R->R , given by f (x) = | x | , is neither one-one nor onto, where | x | is x, if x is positive or 0 and | x | is x , if x is negative.

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

Let the function f:R→R be defined by f(x)=cosx,∀x∈R. Show that f is neither one-one nor onto

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Show that the function f : R rarr R defined by f(x) = cos (5x+3) is neither one-one not onto.

Show that the modulus function f: R->R , given by f(x)=|x| is neither one-one nor onto.

Prove that the Greatest Integer Function f : R->R , given by f (x) = [x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A be the set of all 50 students of class XII in a central school. ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If f:(-pi/2,pi/2)->R and g:[-1,1]->R be defined as f(x)=tanx a...

    Text Solution

    |

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

    Text Solution

    |

  17. Let f,g: R-R be two functions defined as f(x)=|x|+x and g(x)=|x|-x , f...

    Text Solution

    |

  18. Let A={a,b,c,d} and f :A->A be given by f={(a,b),(b,d),(c,a),(d,c)} , ...

    Text Solution

    |

  19. Let f={(3,1),(9,3),(12 ,4)} and g={(1,3),(3,3),(4,9),(5,9)}dot Show th...

    Text Solution

    |

  20. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |