Home
Class 12
MATHS
If f(x) = x^3 + 3x^2 + 12x - 2 sin x, wh...

If `f(x) = x^3 + 3x^2 + 12x - 2 sin x,` where `f: R rarr R,` then (A) f(x) is many-one and onto (B) f(x) is one-one and onto(C) f(x) is one-one and into (D) f(x) is many-one and into

A

f(x) is many-one and onto

B

f(x) is one-one and onto

C

f(x) is one-one and into

D

f(x) is many-one and into

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos
  • FUNCTION

    FIITJEE|Exercise COMPREHENSIONS|8 Videos
  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II|17 Videos
  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos
  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

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

Let f:R rarr R, be defined as f(x)=e^(x^(2))+cos x, then is (a) one-one and onto (b) one-one and into ( c) many-one and onto (d) many-one and into

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

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(x) is (A) one-one and onto (B) one-one and into (C) many-one and onto (D) many-one and into

f: N rarr N, where f(x)=x-(-1)^(x) .Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and onto

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

f: R rarr R,f(x)=x|x| is (A) one-one but not onto (B) onto but not one-one (C) Both one-one and onto (D) neither one-one nor onto

Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the greatest integer less than or equal to x . Then, f(x) is (a) many-one and onto (b) many-one and into (c) one-one and into (d) one-one and onto

Let f:R^(+)rarr{-1,0,1} defined by f(x)=sgn(x-x^(4)+x^(7)-x^(8)-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into one-one and onto (4) one- one and into

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

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I
  1. If f(x)=sqrt(4-x^(2)) +1/(sqrt(abs(sinx)-sinx)), then the-domain of f(...

    Text Solution

    |

  2. If f(x) = x^3 + 3x^2 + 12x - 2 sin x, where f: R rarr R, then (A) f(x)...

    Text Solution

    |

  3. If k sin^(2)x+(1)/(k) cosec^(2) x=2, x in (0,(pi)/(2)), then cos^(2...

    Text Solution

    |

  4. The exhausiive Intervals of real values of x such that sqrt(12-4x)gt1+...

    Text Solution

    |

  5. The range of the function f(x) = sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2], ...

    Text Solution

    |

  6. If fog = abs(sin x) and gof = sin^(2)x then f(x) and g(x) are:

    Text Solution

    |

  7. Let S={(x,y):abs(abs(absx-2)-1)+abs(abs(absy-2)-1)=1). If S is made ou...

    Text Solution

    |

  8. The domain of f(x) = sqrt(log(1//4)((5x-x^(2))/4))+""^(10)C(x) is

    Text Solution

    |

  9. If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  10. function f(x) =sin^(-1)(x-x^2)+sqrt(1-1/|x|+1/[x^2-1]) is defined in t...

    Text Solution

    |

  11. The range of f(x) =sin(sin^(-1){x}). where { ·} denotes the fractional...

    Text Solution

    |

  12. Range of f(x)=cos^(- 1)x+2sin^(- 1)x+3tan^(- 1)x is

    Text Solution

    |

  13. If f(x)=sin(sqrt([a])x) (where [.] denotes the greatest integer functi...

    Text Solution

    |

  14. If f(x)={x, when x is rational, 1-x, when x is irrational , then

    Text Solution

    |

  15. If f:Rto(1,10), where f(x)=(x^(2)+1-alpha)/(x^(2)+2) is an onto functi...

    Text Solution

    |

  16. If f(x)=cos |x| + [|(sinx)/2|], (where [.] denotes the greatest intege...

    Text Solution

    |

  17. The range of function f(x) = sqrt(.^(x^2+4x)C(2x^2+3)) is

    Text Solution

    |

  18. The curve y = f(x) is symmetric about the lines (10^(4)- 1)x + 2(10^(4...

    Text Solution

    |

  19. If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distin...

    Text Solution

    |

  20. lf domain of f(x) is [-1, 2] then domain of f([x]-x^2+4) where [.] den...

    Text Solution

    |