Home
Class 12
MATHS
If the function f : R rarr A given by f(...

If the function `f : R rarr A` given by` f(x) = (x^2)/(x^2+1)` is a surjective then A =

A

R

B

[0, 1]

C

(0, 1]

D

[0, 1)

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS AND EXPRESSION

    HIMALAYA PUBLICATION|Exercise Question Bank|129 Videos
  • STATISTICS MEASURE OF DIPERSION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|28 Videos

Similar Questions

Explore conceptually related problems

The function f : R rarr R defined by f(x) = 7^x + 7^|x| is

The inverse of the function f: R rarr R given by f(x) = log_{a}(x+sqrt(x^2+1)(a gt 0, a ne 1) is

The function f : R//{0} rarr R given by : f(x) = (1)/(x) - (2)/(e^(2x) - 1) can be made continuous at x = 0 by defining f(0) as :

Let R+ be the set of all non-negative real numbers. Show that the function f : R+ rarr [ 4 ,oo ] given by f(x) = x^(2) + 4 is invertible and write the inverse of f.

Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.

Let, f : R rarr R be given by f(x) = tan x . Then f^-1(1) =

If f: R rarr R is defined by f(x)=(x)/(x^(2)+1) find f(f(2))

HIMALAYA PUBLICATION-SETS,RELATIONS AND FUNCTIONS-QUESTION BANK
  1. If f = R rightarrow R is defined by f(x) = |x|, then,

    Text Solution

    |

  2. Let f:[2, oo) rarr X be defined by f(x) = 4x-x^2. Then, f is invertib...

    Text Solution

    |

  3. If the function f : R rarr A given by f(x) = (x^2)/(x^2+1) is a surjec...

    Text Solution

    |

  4. If f(x) = ax+b and g(x) = cx+d then f(g(x)) = g(f(x)) is equivalent to

    Text Solution

    |

  5. If f(x) is defined on [0,1] by the rule f(x) = {(x,if x \ is \ ratio...

    Text Solution

    |

  6. Let f(x) = (ax+b)/(cx+d) . Then fof(x) = x, then

    Text Solution

    |

  7. If f(x) = x^n, n in N and gof(x) = ng(x), then g(x) can be

    Text Solution

    |

  8. The function f : R rarr R given by f(x) = 5-3 sin x

    Text Solution

    |

  9. If g(x) = 1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) =

    Text Solution

    |

  10. The inverse of the function f: R rarr R given by f(x) = log{a}(x+sqrt(...

    Text Solution

    |

  11. If f(x) = log ((1+x)/(1-x)), then f((2x)/(1+x^2))

    Text Solution

    |

  12. If f(x) = (sin^4x+cos^2x)/(sin^2x+cos^4x) for x in R, then f(2013)=

    Text Solution

    |

  13. If f:R rarr R and g : R rarr R are defined by f(x) = 3x + 2 and g(x) ...

    Text Solution

    |

  14. The function f : R rarr R defined by f(x) = 7^x + 7^|x| is

    Text Solution

    |

  15. . If A(1), A(2),…..., A(100) are sets such that n(A(i))= i+2, A(1) sub...

    Text Solution

    |

  16. If A(1) subset A(2) subset A(3) subset .. . . subset A(70) and n(A(i))...

    Text Solution

    |

  17. If A(1) subset A(2) subset A(3) subset .. . subset A(79) and n(A(i))=i...

    Text Solution

    |

  18. Let F1 be the set of parallelograms , F2 the set of rectangles, F3 the...

    Text Solution

    |

  19. Let, S = set of points inside the square T = set of points inside th...

    Text Solution

    |

  20. Two finite sets have m and n elements. The number of subsets of the fi...

    Text Solution

    |