Home
Class 12
MATHS
Find the equivalent definition of f(x...

Find the equivalent definition of
`f(x)=max.{x^(2),(1-x)^(2),2x(1-x)} " where " 0 le x le 1`

A

`f(x)={{:(x^(2),0 le x le 1//3),(2x(1-x),1//3 le x le 2//3),((1-x)^(2), 2//3 le x le 1):}`

B

`f(x)={{:((1-x)^(2), 0 le x le 1//3),(2x(1-x),1//3 le x le 2//3),(x^(2), 2//3 le x le 1):}`

C

`f(x)={{:(x^(2),0 le x le 1//2),((1-x)^(2),1//2 le x le 1):}`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|94 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

Similar Questions

Explore conceptually related problems

Find the equivalent definition of f(x)=max{x^2,(1-x)^2,2x(1-x)} where 0lt=xlt=1

Find the equivalent definition of f(x)=m a xdot{x^2,(-x)^2,2x(1-x)}where 0lt=xlt=1

Consider the function f(x)={(x-[x]-1/2, if x!inI),(0, if x!inI):} where [.] denotes the greatest integer function and g(x)=max. {x^2, f(x), |x|}, -2 le x le 2 . Now answer the question:Area bounded by y=g(x) when -2 le x le 2 is (A) 175/48 (B) 275/48 (C) 175/24 (D) 275/24

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2

Show that the function f(x) = {{:(2x+3",",-3 le x lt -2),(x+1",",-2 le x lt 0),(x+2",",0 le x le 1):} is discontinuous at x = 0 and continuous at every point in interval [-3, 1]

Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if 1 lt x le 2):} at x = 1

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

Find the inverse of each of the following functions : f(x) = {{:(x"," -oo lt x lt 1),(x^(2)"," 1 le x le 4),(2x"," 4 lt x lt oo):}

OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Chapter Test
  1. The set of value of a for which the function f(x)=sinx+[(x^(2))/(a)] d...

    Text Solution

    |

  2. If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt ...

    Text Solution

    |

  3. Find the equivalent definition of f(x)=max.{x^(2),(1-x)^(2),2x(1-x)...

    Text Solution

    |

  4. If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

    Text Solution

    |

  5. The function f(x) is defined in [0,1] . Find the domain of f(t a nx)do...

    Text Solution

    |

  6. The domain of definition of the real function f(x)=sqrt(log(12)x^(2)) ...

    Text Solution

    |

  7. The values of ba n dc for which the identity of f(x+1)-f(x)=8x+3 is sa...

    Text Solution

    |

  8. The function f(x)=sin""(pix)/(2)+2 cos ""(pix)/(3)-tan""(pix)/(4) is p...

    Text Solution

    |

  9. The period of the function sin""((pix)/(2))+cos((pix)/(2)), is

    Text Solution

    |

  10. If x in R, then f(x)=sin^(-1)((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  11. If x in R , then f(x)=cos^(-1)((1-x^(2))/(1+x^(2))) is equal to

    Text Solution

    |

  12. The equivalent definition of the function f(x)=lim(n to oo)(x^(n)-x^(-...

    Text Solution

    |

  13. Find the domain of definitions of the following function: f(x)=log(10)...

    Text Solution

    |

  14. The domain of definition of f(x)=log(0.5){-log(2)((3x-1)/(3x+2))}, is

    Text Solution

    |

  15. Find the domain of the function : f(x)=sqrt(((log)(0. 2)|x-2|)/(|x|))

    Text Solution

    |

  16. The domain of the function y=sqrt(log10(log10x)-log10(4-log10x)-log10 ...

    Text Solution

    |

  17. The function f(x)=log(2x-5)(x^(2)-3x-10) is defined for all belonging ...

    Text Solution

    |

  18. The domain of definition of f(x)=log(1.7)((2-phi'(x))/(x+1))^(1//2), w...

    Text Solution

    |

  19. f(x)=log(100x)((2log(10)x+1)/(-x)) exists, if …. .

    Text Solution

    |

  20. The value of x for which y=log(2){-log(1//2)(1+(1)/(x^(1//4)))-1} is a...

    Text Solution

    |