Home
Class 12
MATHS
f: R to R ,f(x) is differentiable such t...

`f: R to R ,f(x)` is differentiable such that `f(f(x))=k(x^5+x),k!=0)dot` Then `f(x)` is a) always increasing (b) decreasing either increasing or decreasing c) non-monotonic

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

For each of the following graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a.

Find the intervals in which f(x)=x^2+2x-5 is increasing or decreasing.

Let f be continuous and differentiable function such that f(x) and f'(x) has opposite signs everywhere. Then (A) f is increasing (B) f is decreasing (C) |f| is non-monotonic (D) |f| is decreasing

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

Let f(x)=3x+5 then show f(x) is strictly increasing and f^(-1)(x) exists and is strictly increasing for "x"inR

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing

Find the intervals in which the function f given by f(x) = x^(2) – 4x + 6 is (a) increasing (b) decreasing

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot The...

    Text Solution

    |

  2. Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

    Text Solution

    |

  3. f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot ...

    Text Solution

    |

  4. Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^...

    Text Solution

    |

  5. If f: RtoRa n dg: RtoR are two functions such that f(x)+f^(primeprime)...

    Text Solution

    |

  6. Let h(x)=x^(m/n) for x in R , where m and n are odd numbers where 0<...

    Text Solution

    |

  7. Find the number of points of maxima and minima of the function. f(x)=1...

    Text Solution

    |

  8. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

    Text Solution

    |

  9. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

    Text Solution

    |

  10. let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if...

    Text Solution

    |

  11. A cubic f(x) vanishes at x= -2 and has relative minimum and maximum a...

    Text Solution

    |

  12. A window of perimeter P (including the base of the arch) is in the ...

    Text Solution

    |

  13. A point P is given on the circumference of a circle of radius r. Chord...

    Text Solution

    |

  14. Show that 2sinx+tanx≥3x, where 0≤x< π/2 ​

    Text Solution

    |

  15. Find the maxima and minima of the function y=x(x-1)^2,0lt=xlt=2.

    Text Solution

    |

  16. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

  17. The smallest positive root of the equation tanx-x=0 lies in (a)(0,pi/2...

    Text Solution

    |

  18. Let P(x)=a0+a1x^2+a2x^4+...+an x^(2n) be a polynomial in a real variab...

    Text Solution

    |

  19. A cylindrical container is to be made from certain solid material whic...

    Text Solution

    |

  20. Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is po...

    Text Solution

    |