Home
Class 12
MATHS
Cosider f(x)=1-e^((1)/(x)-1) Q. If D i...

Cosider `f(x)=1-e^((1)/(x)-1)`
Q. If `D` is the set of all real `x` such that `f(x)ge0` then `D` is equal to

A

`(-infty,infty)`

B

`(2,infty)`

C

`(-infty,0)cup(1,infty)`

D

`(-1,infty)`

Text Solution

Verified by Experts

The correct Answer is:
B
`1-e^((1)/(x)-1)gt0`
i.e., `e^((1)/(x)-1)lt1`
i.e., `(1)/(x)-1lt0`
i.e., `(x-1)/(x)gt0`
i.e., `x in (-infty,0)cup(1,infty)`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise MATHEMATICS|263 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART - I MATHMATICS|84 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

If D is the set of all real x such that 1-e^((1)/(x)-1) is positive , then D is equal to

Cosider f(x)=1-e^((1)/(x)-1) Q. If S is the range of f(x), then S is

f(x)=e^(x)/([x+1]),x ge 0

consider f:R-{0}toR defined by f(x)=1-e^((1)/(x)-1) Q. f(x) is a/an

Let f(x)=a^(x)-x ln a,a>1. Then the complete set of real values of x for which f'(x)>0 is

If f'(x) gt f(x)" for all "x ge 1 and f(1)=0 , then

if f(x+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

If f(x) =2x +1 and g (x) (x-1)/(2) for all real x, then (fog) ^(-1)( ((1)/(x)) is equal to

Let f(x)=a^(x)-x ln a, a> 1. Then the complete set of real values of x for which f(x)>0 is (a)(1,oo)(b)(-1,oo)(c)(0,oo)(d)(0,1)

RESONANCE-TEST PAPERS-Math
  1. A homogeneous polynomial of the second degree in n variables i.e., the...

    Text Solution

    |

  2. A homogeneous polynomial of the second degree in n variables i.e., the...

    Text Solution

    |

  3. Cosider f(x)=1-e^((1)/(x)-1) Q. If D is the set of all real x such t...

    Text Solution

    |

  4. Cosider f(x)=1-e^((1)/(x)-1) Q. If S is the range of f(x), then S is

    Text Solution

    |

  5. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

    Text Solution

    |

  6. If x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))+ . . . y=(1)/(1^(2))+(3)/(2...

    Text Solution

    |

  7. If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2))...

    Text Solution

    |

  8. lim(n to oo) x^(2)sin(log(e)sqrt(cos((pi)/(x)))) is less then

    Text Solution

    |

  9. f is a continous function in [a, b]; g is a continuous function in [b,...

    Text Solution

    |

  10. Let f(x)="max"(1+s in x ,1,1-cosx),x in [0,2pi],a n dg(x)=max{1,|x-1|}...

    Text Solution

    |

  11. -If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-...

    Text Solution

    |

  12. The function 'g' defined by g(x)= sin(sin^(-1)sqrt({x}))+cos(sin^(-1)s...

    Text Solution

    |

  13. Let A and B be two square matrices satisfying A+BA^(T)=I and B+AB^(T)=...

    Text Solution

    |

  14. Let f(x)=[x][sinx]+[-x][-sinx]+x+[-x][sinx]+[x][-sinx], where [.] dent...

    Text Solution

    |

  15. Draw the graph of f(x) =cot^(-1)((2-|x|)/(2+|x|)).

    Text Solution

    |

  16. Comprehension 2 Consider the system of linear equations alphax+y...

    Text Solution

    |

  17. Let f:RtoR be defined as f(x)=(2x-3pi)^(3)+(4)/(3)x+cosx and g(x)=f^(-...

    Text Solution

    |

  18. if A[{:(5,-3),(111,336):}] and det(-3A^(2013)+A^(2014))=alpha^(alpha)+...

    Text Solution

    |

  19. if lim(xto0) (ae^(2x)-bcos2x+ce^(2x)-xsinx)/(xsinx)=1 and f(t)=(a+b)t^...

    Text Solution

    |

  20. Let f(x)={{:(3^x","-1lexle1),(4-x","1ltxle4):} then

    Text Solution

    |