Home
Class 12
MATHS
if the function f:R to R be defined by f...

if the function `f:R to R` be defined by `f(x)=tanx-x,` then f(x) always

A

increases

B

decreases

C

remains constant

D

becomes zero

Text Solution

Verified by Experts

The correct Answer is:
A
Given, f(x)=tanx-x
`impliesf'(x)=sec^(2)x-1`
`=(1-cos^(2)x)/(cos^(2)x)`
Since `0 le cos^(2)x le 1, AA x`
`thereforef'(x)gt0` for all values of x.
thus, f(x) is always increasing.
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 03

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|49 Videos

  • PRACTICE SET 05

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

The function f:R rarr R be defined by f(x)=2x+cos x then f

The function f:R rarr R is defined by f(x)=3^(-x)

The function f: R to R defined by f(x) = 4x + 7 is

If f:R to R is defined by f(x)=|x|, then

the function f:R rarr R defined as f(x)=x^(3) is

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

If a function f: R to R is defined as f(x)=x^(3)+1 , then f is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 04-PAPER 2 (MATHMATICS)
  1. Gas is being pumped into a a spherical balloon at the rate of 30 ft^(3...

    Text Solution

    |

  2. The vectors which is/are coplanar with vectors hati+hatj+2hatk and hat...

    Text Solution

    |

  3. if the function f:R to R be defined by f(x)=tanx-x, then f(x) always

    Text Solution

    |

  4. int(0)^(pi)(xdx)/(1+sinx) is equal to

    Text Solution

    |

  5. If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3...

    Text Solution

    |

  6. The sum to infinity of the series 1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^...

    Text Solution

    |

  7. A straight line passes through the points (5,0) and (0,3). The length ...

    Text Solution

    |

  8. The ratio by which the line 2x + 5y -7=0 divides the straight line joi...

    Text Solution

    |

  9. Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroi...

    Text Solution

    |

  10. A hyperbola passes through a focus of the ellipse x^2/169 + y^2/25=1. ...

    Text Solution

    |

  11. If A=[(1,-2,1),(2,1,3)] and B=[(2,1),(3,2),(1,1)] then (AB)' is equal ...

    Text Solution

    |

  12. If equation 4x^(2)+2pxy+25y^(2)+2x+5y-1=0 represents parallel lines,...

    Text Solution

    |

  13. A bag contains 5 brown and 4 white socks. A man pulls out two socks. ...

    Text Solution

    |

  14. The fucntion f(x)=x+cos x is

    Text Solution

    |

  15. The logically equivalent proposition of p iff q is

    Text Solution

    |

  16. If vec u ,"" vec v , vec w are noncoplanar vectors and p, q are re...

    Text Solution

    |

  17. int(-1)^(0)(dx)/(x^(2)+2x+2) is equal to

    Text Solution

    |

  18. A particle moves along the curve y=x^2+2xdot At what point(s) on the c...

    Text Solution

    |

  19. If alpha=x(a xxb)+y(b xxc)+z(cxxa) and [abc]=(1)/(8), then x+y+z is eq...

    Text Solution

    |

  20. The angle between the lines x=1, y=2 and y=-1, z=0 is

    Text Solution

    |