Home
Class 12
MATHS
If f: R to R is given by f(x)=(x^2-4)/(x...

If `f: R to R` is given by `f(x)=(x^2-4)/(x^2+1)` , identify the type of function.

Text Solution

Verified by Experts

The correct Answer is:
many-one, into

`f(x)=f(-x), " So, "f` is many-one.
Also, `f(x)=1-(5)/(x^(2)+1) in [-4,1) " So, "f` is into.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f : R to R be defined as f(x) = (x^2-x+4)/(x^2+x+4) . Then the range of the function f(x) is

Let f:R to R be given by f(x) =|x^(2)-1|, x in R . Then

Show that f: [-1, 1] to R, given by f (x) = (x)/((x +2)) is one-one. Find the inverse of the function f : [-1, 1] to Rangle f.

If f:R to R given by f(x)=x^(3)+px^(2)+qx+r, is then find the condition for which f(x) is one-one.

A function f : R to R is defined by f(x) =x^(2) .Then show that f is neither nor surfection .

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

The function f:R to R is defined by f(x)=cos^(2)x+sin^(4)x for x in R . Then the range of f(x) is

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

A function f:R to R is defined by f(x)=(x-1)(x-2) . Which one of the following is correct in respect of the function?

Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Which of the following function from Z to itself are bijections? f(x)=...

    Text Solution

    |

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

    Text Solution

    |

  3. If f: R to R is given by f(x)=(x^2-4)/(x^2+1) , identify the type of f...

    Text Solution

    |

  4. If f: RtoS , defined by f(x)=sinx-sqrt(3)cosx+1,is onto , then find t...

    Text Solution

    |

  5. Let g: Rvec(0,pi/3) be defined by g(x)=cos^(-1)((x^2-k)/(1+x^2)) . The...

    Text Solution

    |

  6. Identify the type of the function f:R to R, f(x)=e^(x^(2))+cosx.

    Text Solution

    |

  7. Let a function f:R to R be defined by f(x)=2x+cosx+sinx " for " x in ...

    Text Solution

    |

  8. If f:R to R given by f(x)=x^(3)+px^(2)+qx+r, is then find the conditi...

    Text Solution

    |

  9. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

    Text Solution

    |

  10. Find the range of f(x)=(x^2+34 x-71)/(x^3+2x-7)

    Text Solution

    |

  11. Find the range of f(x)=sqrt(x-1)+sqrt(5-x)

    Text Solution

    |

  12. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of ...

    Text Solution

    |

  13. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  14. Find the domain of f(x)=sqrt(sinx)+sqrt(16-x^2)

    Text Solution

    |

  15. Solve sinx > -1/2

    Text Solution

    |

  16. Prove that the least positive value of x , satisfying tanx=x+1,lies i...

    Text Solution

    |

  17. Find the range of f(x)=sec(pi/4cos^2x)

    Text Solution

    |

  18. If x in [1,2] , then find the range of f(x)=tanx

    Text Solution

    |

  19. Find the range of f(x)=1/(1-3sqrt(1-sin^2x))

    Text Solution

    |

  20. Find the range of f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1)

    Text Solution

    |