Home
Class 12
MATHS
What is the equivalent definition of the...

What is the equivalent definition of the function given by
`{:f(x)={(2x",",xge0),(0",",lt0):}`

A

`f(x)=|x|`

B

`f(x)=2x`

C

`f(x)=|x|+x`

D

`f(x)=2|x|`

Text Solution

Verified by Experts

The correct Answer is:
C
The given function is `{:f(x)={(2x",",xge0),(0",",xlt0):}`
The equation can be re-written as
`{:f(x)={(x+x",",xge0),(-x+x," "xlt0):}`
Hence, equivalent definition of given function is `f(x)=|x|+x`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

Discuss the continuity of the function : f(x)={{:(x",if "xge0),(x^(2)",if "xlt0):}

Discuss the continuity of the function f(x) ={(x", " x ge 0),(2", "x lt0):} at x=0

Consider the following in respect of the function f(x)={{:(2+x","xge0),(2-x","xlt0):} 1. lim_(x to 1) f(x) does not exist. 2. f(x) is differentiable at x=0 3. f(x) is continuous at x=0 Which of the above statements is /aer correct?

Draw the graph of the modulus function, defined by f:RtoR:f(x)=|x|={{:(x",when "xge0),(-x",when "xlt0):}

Consider the following in respect of the function f(x)={{:(2+x,xge0),(2-x,xlt0):} 1. underset(xrarr1)limf(x) does not exist 2. f(x) is differentiable at x = 0 3. f(x) is continuous at x = 0 Which of the above statements is / are correct?

Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x lt0 ),(x+1 ", " x ge0):}, at =0.

The point(s), at which the function f given by f(x) = {{:((x),xlt0),(-1,xge0):} is continuous, is/are:

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Given f(x)=log[((1+x))/((1-x))]andg(x)=((3x+x^(2)))/((1+3x^(2))), then...

    Text Solution

    |

  2. What is the value of lim(xto0) (sin|x|)/(x)?

    Text Solution

    |

  3. What is the equivalent definition of the function given by {:f(x)={(...

    Text Solution

    |

  4. If f:RtoR^(+) such that f(x)=(1//3)^(x), the what is the value of f^(-...

    Text Solution

    |

  5. What is the value of lim(x to 0) (xsin5x)/(sin^(2)4x)

    Text Solution

    |

  6. If f(x)=(1+x)^(5//x) is continuous at x=0, then what is the value of f...

    Text Solution

    |

  7. Consider the following statements: 1. The function f(x) = greatest i...

    Text Solution

    |

  8. If lim(x to a) [(f(x))/(g(x))] exists, then which one of the following...

    Text Solution

    |

  9. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

    Text Solution

    |

  10. The above curve shows the graph of a^(x) under which one of the follow...

    Text Solution

    |

  11. If f(x)=log((1+x)/(1-x)), "then f "((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  12. If f(x)=(x+1)^(cotx) is continuous at x=0, then what is f(0) equal to?

    Text Solution

    |

  13. What is the value of lim(xtooo) ((x-2)/(x+2))^(x+2) = ?

    Text Solution

    |

  14. If the derivative of the function f(x) ={ax^2+b , x lt -1 and bx^2 ...

    Text Solution

    |

  15. If f(x) is differentiable everywhere, then which one of the following ...

    Text Solution

    |

  16. Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are...

    Text Solution

    |

  17. If (x-a)/(b+c)+(x-b)/(c+a)+(x-c)/(a+b)=3 then value of x is

    Text Solution

    |

  18. If -x^(2)+3x+4gt0, then which one of the following is correct?

    Text Solution

    |

  19. Given f(x)=x+(1)/(x), then what is f^(2)(x) equal ot ?

    Text Solution

    |

  20. If f(x)={{:(1,x" is a rational number"),(0",","x is an irrational numb...

    Text Solution

    |