Home
Class 12
MATHS
If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+...

If `f:R->R` and `f(x)=sin(pi{x})/(x^4+3x^2+7)`, where `{}` is a fractional part of x , then

A

f is injective

B

f is not one-one and non-constant

C

f is a surjective

D

f is a zero function

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

Period of the function f(x)=sin(sin(pix))+e^({3x}) , where {.} denotes the fractional part of x is a. 1 " " b. 2 c. 3 " " d. none of these

Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fractional part of x. Then, which of the following is/are correct?

Discuss the minima of f(x)={x}, where {,} denotes the fractional part of x

Let f:R rarr R be a function defined by f(x)={abs(cosx)} , where {x} represents fractional part of x. Let S be the set containing all real values x lying in the interval [0,2pi] for which f(x) ne abs(cosx) . The number of elements in the set S is

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. f:R rarr R and f(x)=(x(x^(4)+1)(x+1)+x^(4)+2)/(x^(2)+x+1) , then f(x) is

Let f(x) = x - x^(2) and g(x) = {x}, AA x in R where denotes fractional part function. Statement I f(g(x)) will be continuous, AA x in R . Statement II f(0) = f(1) and g(x) is periodic with period 1.

The value of int_(-5)^(5)f(x)dx, where f(x)="minimum"({x+1},{x-1}), ∀ x in R and {.} denotes fractional part of x, is equal to

If f(x) = {{:(x+{x}+x sin {x}",","for",x ne 0),(0",","for",x = 0):} , where {x} denotes the fractional part function, then

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-(x))dot Show that g(...

    Text Solution

    |

  2. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

    Text Solution

    |

  3. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  4. A function f from integers to integers is defined as f(x)={{:(n+3, n ...

    Text Solution

    |

  5. If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+7), where {} is a fractional p...

    Text Solution

    |

  6. Show that f: R→ R defined as f(a) = 3a – 4 is one to one function.

    Text Solution

    |

  7. Find dy/dx if y= 3^x

    Text Solution

    |

  8. Let y be element of the set A={1,2,3,,5,6,10,15,30} and x(1),x(2),x(3)...

    Text Solution

    |

  9. If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax...

    Text Solution

    |

  10. f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall x in R is a one-one function,...

    Text Solution

    |

  11. If two roots of the equation (p-1)(x^2 +x +1)^2 -(p+1)(x^4+x^2+1)=0 ar...

    Text Solution

    |

  12. If f(x)=x^11+x^9−x^7+x^3+1 and f(sin^(−1)(sin8))=α,α is constant, then...

    Text Solution

    |

  13. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

    Text Solution

    |

  14. The complete set of values of a for which the function f(x)=tan^(-1)(x...

    Text Solution

    |

  15. The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(si...

    Text Solution

    |

  16. The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is ...

    Text Solution

    |

  17. The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal ...

    Text Solution

    |

  18. The domain of the function f(x)=root(6)(4^(x)+8^(2//3(x-2))-52-2^(2(...

    Text Solution

    |

  19. The domain of derivative of the function f(x)=abs(sin^(-1)(2x^(2)-1)...

    Text Solution

    |

  20. The range of a function f(x)=tan^(-1){log(5//4)(5x^(2)-8x+4)} is

    Text Solution

    |