Home
Class 12
MATHS
Let f :RrarrR be a function defined by f...

Let `f :RrarrR` be a function defined by `f(x) = x^3 + x^2 + 3x + sin x`. Then f is

A

One-one end into

B

One-one and onto

C

Many-one and into

D

many-one and onto

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise ONE OR MORE THAN ONE ANSWE IS/ARE CORRECT|23 Videos

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise COMPREHENSION TYPE PROBLEMS|13 Videos

  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

Let f : R → R be a function defined by f ( x ) = 2 x − 5 ∀ x ∈ R . Then Write f^(−1) .

Let f:R->R be a function defined by f(x)=x^2-(x^2)/(1+x^2) . Then:

If f:R to R be the function defined by f(x) = sin(3x+2) AA x in R. Then, f is invertible.

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

Let f: R to R be a function defined as f (x) = 3x+ 7 , x in R . Show that f is an onto functions.

Let f:R→R be a function defined by f(x)= \frac{ x ^ { 2 } -8 }{ x ^ { 2 } +2 } ​Then f is

Let f: R-> R be the function defined by f(x)=4x−3 for all x in R . Then write f^-1 .

Let f be a real-valued function defined by f(x) = 3x^(2) + 2x + 5 Find f'(1).

Let the funciton f:R to R be defined by f(x)=2x+sin x . Then, f is

let f: RrarrR be a function defined by f(x)=max{x,x^3} . The set of values where f(x) is differentiable is:

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. Let f :RrarrR be a function defined by f(x) = x^3 + x^2 + 3x + sin x. ...

    Text Solution

    |

  2. Let f (x) be a polynomial of degree 6 with leading coefficient 2009, S...

    Text Solution

    |

  3. Let f(x)=x^(3)-3x+1. Then number of different real solutions of f(f(x)...

    Text Solution

    |

  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

    Text Solution

    |

  6. The number of elements in the range of the function : y =sin ^(-1) [...

    Text Solution

    |

  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

    Text Solution

    |

  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

    Text Solution

    |

  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  12. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  13. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  14. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  15. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  16. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  17. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  18. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  19. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  20. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  21. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |