Home
Class 12
MATHS
Let f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4...

Let `f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):}`
and `g(x)={{:(x-3",", x lt 4),(x^(2)+2x+2",", x le 4):}`, which one of the following is/are true?

A

(f+g)(3.5)=0

B

f(gh(3))=3

C

f(g(2))=1

D

(f-g)(4)=0

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|25 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|76 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):} , then g(x) = f(|x|) is

Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(-cos x -1 "," pi//2 lt x le pi):} which one of the following is not true ?

Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of 4(gof) (2) - (fog) (9) is

Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of (gof) (0) + (fog) (-3) is

ARIHANT MATHS-FUNCTIONS-Exercise (More Than One Correct Option Type Questions)
  1. f(x)=cos^(2)x+cos^(2)(pi/3+x)-cosx*cos(x+pi/3) is

    Text Solution

    |

  2. If the following functions are defined from [-1,1]to[-1,1], select tho...

    Text Solution

    |

  3. Let f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):} and g(x)={{:(...

    Text Solution

    |

  4. If f(x)=x^(2)-2ax+a(a+1),f:[a,infty) rarr [a,infty). If one of the sol...

    Text Solution

    |

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

    Text Solution

    |

  6. The graph of f:R rarr R defined by y=f(x) is symmetric with respect to...

    Text Solution

    |

  7. Let f be the continuous and differentiable function such that f(x)=f(2...

    Text Solution

    |

  8. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then

    Text Solution

    |

  9. Let A={1,2,3,4,5}, B={1,2,3,4) and f:A rarr B is a function, the

    Text Solution

    |

  10. In a function 2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]...

    Text Solution

    |

  11. If f(x) is a differntiable function satisfying the condition f(100x)=x...

    Text Solution

    |

  12. If [x] denotes the greatest integer function then the extreme values o...

    Text Solution

    |

  13. Which of the following is/are periodic?

    Text Solution

    |

  14. If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,......

    Text Solution

    |

  15. Let f:R rarr R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3), fora...

    Text Solution

    |

  16. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

    Text Solution

    |

  17. If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y i...

    Text Solution

    |

  18. lf the fundamental period of function f(x)=sinx + cos(sqrt(4-a^2))x is...

    Text Solution

    |

  19. Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f...

    Text Solution

    |

  20. if f(g(x)) is one-one function, then (1) g(x) must be one- one (2) f(x...

    Text Solution

    |