Home
Class 12
MATHS
Let f(x) =ax^(2) + bx + c and f(-1) lt 1...

Let `f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a ne 0`, then

A

`g(f(x+1))gtf(f(x-1))`

B

`f(g(x-1))gtf(f(x+1))`

C

`g(f(x+1))ltg(f(x-1))`

D

`g(f(x+1))ltg(g(x-1))`

Text Solution

Verified by Experts

The correct Answer is:
2,3
Since g(x) is increasing and f(x) is decreasing
`g(x+1)gtg(x-1)and f(x+1)ltf(x-1)`
or `f{g(x+1)}ltf{(g(x-1)}`
and `g{f(x+1)}ltg{f(x-1)}`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Linked comprehension type|8 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|93 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If f(x)=ax^(2)+bx+c, f(-1) gt (1)/(2), f(1) lt -1 and f(-3)lt -(1)/(2) , then

Let f(x)=ax^(2)+bx+c, if f(-1) -1,f(3)<-4 and a!=0 then

If f(x)=ax^(2)+bx+c and f(-1) ge -4 , f(1) le 0 and f(3) ge 5 , then the least value of a is

If f(x^(2) - 4x + 4) = x^(2) + 1 . Find f(1) if f(1) lt 8 .

Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in R. Also given that f (x) =0 has no real roots and 4a + b gt 0. Let p =b-4a, q=2a +b, then pq is:

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Multiple)
  1. Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x)...

    Text Solution

    |

  2. The function y=(2x-1)/(x-2),(xne 2)

    Text Solution

    |

  3. Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a...

    Text Solution

    |

  4. If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1...

    Text Solution

    |

  5. If f'(x) = g(x) (x-a)^2, where g(a) != 0 and g is continuous at x = a,...

    Text Solution

    |

  6. The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2...

    Text Solution

    |

  7. Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1). Then f(x) has local extrem...

    Text Solution

    |

  8. Let f(x)=sinx+ax+b.Then which of the following is/are true?

    Text Solution

    |

  9. The function (sin(x+a))/(sin(x+b)) has no maxima or minima if b-a=npi...

    Text Solution

    |

  10. Consider f(x)=ax^(4)+cx^(2)+dx+e has no point o inflection Then which ...

    Text Solution

    |

  11. L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/7 Then at x=1/2, whi...

    Text Solution

    |

  12. In which of the following graphs is x =c point of inflection?

    Text Solution

    |

  13. Let f(x) be an increasing function defined on (0,oo) . If f(2a^2+a+1)>...

    Text Solution

    |

  14. If f(x)=(sin^2x-1)^("n"),"" then x=pi/2 is a point of local maximum, i...

    Text Solution

    |

  15. For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the followi...

    Text Solution

    |

  16. Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , where ai ' s are real and f(x)=...

    Text Solution

    |

  17. If f(x)a n dg(x) are two positive and increasing functions, then which...

    Text Solution

    |

  18. An extremum of the function f(x)=(2-x)/picospi(x+3)+1/(pi^2)sinpi(x+3)...

    Text Solution

    |

  19. For the function f(x)=x^4(12(log)e x-7), the point (1,7) is the point...

    Text Solution

    |

  20. Let f(x)=log(2x-x^2)+sin(pix)/2dot Then which of the following is/are ...

    Text Solution

    |