Home
Class 11
MATHS
The function f:[0,3]vec[1, 29], defined ...

The function `f:[0,3]vec[1, 29],` defined by `f(x)=2x^3-15 x^2+36 x+1,` is one-one and onto onto but not one-one one-one but not onto neither one-one nor onto

A

one-one and onto

B

onto but not one-one

C

one-one but not onto

D

neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `f(x)=2x^(3)-15x^(2)+36x+1`
`f'(x)=6x^(2)-30x+36=6(x-3)(x-2)`
`"Clearly", f'(x) gt 0" for x in (0,2)and f'(x) lt 0"For x" in (2,3)"`
So, f'(x) is increasing on (0,2) and decreasing (2,3).
Also, f(0)=1,f(2)=29 and f(3)=28
As f is a continous function. So, it attains every value between its minimum value 1 and maximum value `f(2)=29`, So, f is onto and it is not one-one
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|48 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

The function f:[0,3]->[1,29] , defined by f(x)=2x^3−15x^2+36x+1 , is (a) one-one and onto (b) onto but not one-one (c) one-one but not onto (d) neither one-one nor onto

If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one-one but not onto (b) onto but not one-one (c) both one and onto (d) neither one-one nor onto

The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto

If f:[0,oo)->[0,oo) and f(x)=x/(1+x), then f(x) is (a) one-one and onto (b)one-one but not onto (c)onto but not one-one (d)neither on-one nor onto

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-one but not onto (b) many-one but onto (c) one-one and onto (d) neither one-one nor onto

Let M be the set of all 2xx2 matrices with entries from the set R of real numbers. Then the function f: M->R defined by f(A)=|A| for every A in M , is (a) one-one and onto (b) neither one-one nor onto (c) one-one but not onto (d) onto but not one-one

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Section I - Solved Mcqs
  1. Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the gre...

    Text Solution

    |

  2. Let M be the set of all 2xx2 matrices with entries from the set R o...

    Text Solution

    |

  3. The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and on...

    Text Solution

    |

  4. Two functions f:R to R and g:Rto R are defined as follows: f(x)={{:(...

    Text Solution

    |

  5. The range of the function f(x)=\ ^(7-x)P(x-3) is (a) {1, 2, 3, 4, ...

    Text Solution

    |

  6. A function f from the set of natural numbers to the set of integers...

    Text Solution

    |

  7. Let f:(-1,1)vecB be a function defined by f(x)=tan^(-1)(2x)/(1-x^2) . ...

    Text Solution

    |

  8. Let f: N->Y be a function defined as f(x)=4x+3 , where Y={y in N : y=...

    Text Solution

    |

  9. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

    Text Solution

    |

  10. If X and Y are two non-empty sets, where f:X rarr Y, is function is de...

    Text Solution

    |

  11. For real x, let f(x)=x^(3)+5x+1, then

    Text Solution

    |

  12. Let f:(0,1) rarr R be defined by f(x)=(b-x)/(1-bx), where b is a const...

    Text Solution

    |

  13. The function f:[0,3]vec[1, 29], defined by f(x)=2x^3-15 x^2+36 x+1, is...

    Text Solution

    |

  14. For a real number x let [x] denoutes the greatest interger less than o...

    Text Solution

    |

  15. If P(S) denotes the set of all subsets of a given set S, then the numb...

    Text Solution

    |

  16. f: { 1, 2, 3, 4} -> {1, 4, 9, 16} and g: {1, 4. 9, 16) ->{1,1/2,1/3,1/...

    Text Solution

    |

  17. In the above example (gof)^(-1)((1)/(4)) is equa to

    Text Solution

    |

  18. If a real polynomial of degree n satisfies the relation f(x)=f(x)f''(x...

    Text Solution

    |

  19. If the function f:[1,\ oo)->[1,\ oo) defined by f(x)=2^(x(x-1)) is inv...

    Text Solution

    |

  20. The function f:R to [-(1)/(2),(1)/(2)] defined as f(x)=(x)/(1+x^(2)), ...

    Text Solution

    |