Home
Class 12
MATHS
Let f: R R be a continuous function ...

Let f: R R be a continuous function defined by `f(x)""=1/(e^x+2e^(-x))` . Statement-1: `f(c)""=1/3,` for some `c in R` . Statement-2: `0""<""f(x)lt=1/(2sqrt(2)),` for all `x in R` . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

A

Statement -1 is true , Statement -2 is true , Statement-2 is not a correct explanation for statement -1.

B

Statement-1 is true Statement -2 is false.

C

Statement-1 is false , Statement-2 is treu

D

Statement -1 is true Statement -2 is true, Statement -2 is a correct explanation for statement -1.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part I|27 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f'(1)=

Let f:R rarr R be the function defined by f(x)=x^(3)+5 then f^(-1)(x) is

Let f:R rarr R be a function defined by,f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)) then

Let f:R to R be the function defined by f(x)=2x-3, AA x in R. Write f^(-1).

Let f:R rarr R be a function is defined by f(x)=x^(2)-(x^(2))/(1+x^(2)), then

The function f :R to R defined by f (x) = e ^(x) isd

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

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part II
  1. Find the shortest distance between the line x - y +1 = 0 and the curve...

    Text Solution

    |

  2. Let f : R to R be defined by if (x)= {underset(2x + 3 " ", " "i...

    Text Solution

    |

  3. Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-...

    Text Solution

    |

  4. The equation of the tangent to the curve y""=""x""+4/(x^2) , that is p...

    Text Solution

    |

  5. Let f be a function defined by - f(x) ={underset(1" "," ...

    Text Solution

    |

  6. The shortest distance between line y-x=1 and curve x=y^2 is

    Text Solution

    |

  7. A spherical balloon is filled with 4500p cubic meters of helium gas...

    Text Solution

    |

  8. Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""...

    Text Solution

    |

  9. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

    Text Solution

    |

  10. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  11. If x = -1 and x = 2 are extreme points of f(x) = alpha log|x| + beta x...

    Text Solution

    |

  12. A wire of length 2 units is cut into two parts which are bent respe...

    Text Solution

    |

  13. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

    Text Solution

    |

  14. Twenty metres of wire is available for fencing off a flower-bed in ...

    Text Solution

    |

  15. The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve i...

    Text Solution

    |

  16. The radius of a circle, having minimum area, which touches the curv...

    Text Solution

    |

  17. If the curves y^2=6x, 9x^2+by^2=16 intersect each other at right angle...

    Text Solution

    |

  18. Let f(x)=x^2+(1/x^2) and g(x)=x-1/x xinR-{-1,0,1}. If h(x)=(f(x)/g(x)...

    Text Solution

    |

  19. Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C b...

    Text Solution

    |

  20. A helicopter flying along the path y=7+x^((3)/(2)), A soldier standint...

    Text Solution

    |