Home
Class 12
MATHS
Which of the following function from Z t...

Which of the following function from Z to itself are bijections? `f(x)=x^3` (b) `f(x)=x+2` `f(x)=2x+1` (d) `f(x)=x^2+x`

Text Solution

Verified by Experts

Correct option is B)
`(A) f(x)=x^3`
one−one test:
Let `x1`​ and `x2`​ be the
elements in the domain such that,
`f(x_1​)=f(x_2​)`
`⇒ (x_1)^3​=(x_2)^3​`
`⇒ x_1​=x_2​`
∴ f is one-one.
...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

Which of the following function from Z to itself are bijections? f(x)=x^(3)( b) f(x)=x+2f(x)=2x+1( d )f(x)=x^(2)+x

Which of the following functions from A={x in R :-1lt=xlt=1} to itself are bijections? f(x)=|x| (b) f(x)=sin(pix)/2 (c) f(x)=sin(pix)/4 (d) none of these

Let A=[-1,1]. Then,discuss whether the following functions from A to itself are one-one onto or bijective: f(x)=(x)/(2) (ii) g(x)=|x|quad (iii) h(x)=x^(2)

Let A=[-1,1]. Then,discuss whether the following functions from A to itself are one- one,onto or bijective: f(x)=(x)/(2) (ii) g(x)=|x|( iii) h(x)=x^(2)

Which of the following function is non- differentiable in domain? f(x)=(x-2)/(x^(2)+3) (b) f(x)=log|x|f(x)=x^(3)log x(d)f(x)=(x-3)^((3)/(5))

Which of the following functions is the inverse of itself? f(x)=(1-x)/(1+x) (b) f(x)=5^(log x)f(x)=2^(x(x-1))(d) None of these

Examine the following functions for continuity. (a) f(x)=x-5 (b) f(x)=1/(x-5) (c) f(x)=(x^2-25)/(x+5) (d) f(x)=|x-5|

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

Which of the following function is surjective but not injective.(a) f:R rarr R,f(x)=x^(4)+2x^(3)-x^(2)+1(b)f:R rarr R,f(x)=x^(2)+x+1(c)f:R rarr R^(+),f(x)=sqrt(x^(2)+1)(d)f:R rarr R,f(x)=x^(3)+2x^(2)-x+1

Which of the following functions has inverse function? f:Z rarr Z defined by f(x)=x+2f:Z rarr Z defined by f(x)=2xf:Z rarr Z defined byy f(x)=xf:Z rarr Z defined by f(x)=|x|

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. A function f from the set of natural numbers to integers is defined by...

    Text Solution

    |

  2. Let f be an injective map. with domain (x, y, z and range (1, 2, 3), s...

    Text Solution

    |

  3. Which of the following function from Z to itself are bijections? f(x)=...

    Text Solution

    |

  4. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

    Text Solution

    |

  5. Let A}x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is a bije...

    Text Solution

    |

  6. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  7. If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one...

    Text Solution

    |

  8. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=sin^(-...

    Text Solution

    |

  9. Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(...

    Text Solution

    |

  10. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!...

    Text Solution

    |

  11. Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is...

    Text Solution

    |

  12. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |

  13. The function f: R->R , f(x)=x^2 is (a) injective but not surjective (b...

    Text Solution

    |

  14. A function f from the set of natural numbers to integers defined by...

    Text Solution

    |

  15. Which of the following functions from A={x in R :-1lt=xlt=1} to it...

    Text Solution

    |

  16. Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s...

    Text Solution

    |

  17. The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and on...

    Text Solution

    |

  18. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation f...

    Text Solution

    |

  19. If f(x)=3x-5, then f^(-1)(x) is given by 1/((3x-5)) is given by ((x+...

    Text Solution

    |

  20. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then f(x)=sin^2x ,g(x)...

    Text Solution

    |