Home
Class 12
MATHS
Consider the following statements : 1....

Consider the following statements :
1. If `f(x)=x^(2)andg(y)=y^(3)` then f=g.
2. Identity function is not always a bijection.
Which of the above statements is/are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
B

(1) `f(x)=x^(3)andg(y)=y^(3)`
`implies` f=g is a corrent statement.
(2) Identify function is always a bijection.
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

Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} Consider the following statements : 1. The function is discontinuous at x=3. 2. The function is not differentiable at x=0. What of the above statements is/are correct?

Read the following information carefully and answer the question given below: Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} Consider the following statements: I. The function is discontinuous at x = 3 II. The function is not differentiable at x = 0 Which of the above statement(s) is/are correct?

Consider the following statements in respect of f(x)=|x|-1 : 1. f(x) is continuous at x=1. 2. f(x) is differentiable at x=0. Which of the above statement is/are correct?

Consider the following statements: 1. The function f(x)=|x| is not differentiable at x=1. 2. The function f(x)=e^(x) is not differentiable at x=0. Which of the above statements is/are correct ?

Let f(x) be a function defined in 1lexleoo by f(x)={{:(2-x" for "1lexle2),(3x-x^(2)" for "xgt2):} Consider the following statements : 1. f'(2+0) does not exist. 2. f'(2-0) does not exist. Which of the above statements is/are correct?

Consider the following statements: I. The function f(x)=|x| is not differentiable at x = 1 II. The function f(x)=e^(x) is differentiable at x = 0 Which of the above statements is/are correct?

Consider the following statements 1 f(x)=In x is an increasing funciton on (0,oo) 2 f(x) =e^(x)-x(In x) is an increasing function on (1,oo) Which of the above statement is / are correct ?

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. What is lim(xto2) (x-2)/(x^(2)-4) equal to?

    Text Solution

    |

  2. Let f:RtoR be a function whose inverse is (x+5)/(3). What is f(x) equa...

    Text Solution

    |

  3. Consider the following statements : 1. If f(x)=x^(2)andg(y)=y^(3) th...

    Text Solution

    |

  4. Let A={x""inR|xge0|. A function f:AtoA is defined by f(x)=x^(2). Which...

    Text Solution

    |

  5. Consider the following statement in respect of a function f(x): 1. f...

    Text Solution

    |

  6. Consider the function f(x)={{:(x^(2)",",xgt2),(3x-2",",xle2):}. Which ...

    Text Solution

    |

  7. Consider the following statements: 1. lim(xto0)sin""(1)/(x) does not...

    Text Solution

    |

  8. lim(x to 0) (sinx-tanx)/(x) equal to?

    Text Solution

    |

  9. What is lim(x to 0) (1-sqrt(1+x))/(x) equal to?

    Text Solution

    |

  10. Consider the following statements: 1. The derivative where the funct...

    Text Solution

    |

  11. Let N be the set of natural numbers and f : N->N be a function given b...

    Text Solution

    |

  12. Let f be a function from the set of natural numbers to the set of even...

    Text Solution

    |

  13. Consider the following function : 1. f(x)=e^(x),"where "xgt0 2. g(...

    Text Solution

    |

  14. What is lim(x to 2) (2-x)/(x^(3)-8) equal to ?

    Text Solution

    |

  15. A function f:RtoR is defined as f(x)=x^(2)" for "xge0,f(x)=-x" for "xl...

    Text Solution

    |

  16. What is lim(xto0) (1-cosx)/(x) equal to ?

    Text Solution

    |

  17. What is lim(xto0) (cosx)/(pi-x) equal to ?

    Text Solution

    |

  18. What is lim(xto0) (sin2x+4x)/(2x+sin4x) equal to ?

    Text Solution

    |

  19. Let N denote the set of all non-negative integers and Z denote the set...

    Text Solution

    |

  20. What is lim(xto0) ((1+x)^(n)-1)/(x) equal to ?

    Text Solution

    |