Home
Class 12
MATHS
Examine the function, f(x) = {{:(x - 1",...

Examine the function, `f(x) = {{:(x - 1",",x lt 0),(1//4",",x = 0),(x^(2)-1",",x gt 0):}` Discuss the continuity and if discontinuous remove the discontinuity.

Text Solution

Verified by Experts

The correct Answer is:
`rArr" "f(x) = {{:(x -1",",x lt 0),(-1",",x = 0),(x^(2)-1",",x gt 0):}`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(2x+3",","when",x lt 0),(0",","when",x = 0),(x^(2)+3",","when",x gt 0):} Discuss the continuity.

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]

Show that the function f(x) = {{:(2 + x"," , "if " x ge 0),(1",", "if " x lt 0):} is not continuous at x = 0

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is

Consider the piecewise defined function f(x) = {{:(sqrt(-x),"if",x lt 0),(0,"if",0 le x le 4),(x - 4,"if",x gt 4):} describe the continuity of this function.

Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0):} at x = 0

Examine for continuity the following functions: f(x) = {:(x , if x ne 0),(1 , if x = 0):}

Prove that the function f(x) = {:{((sinx)/x , x < 0),(x^2 +1, x ge0):} is continuous.

Examine for continuity the function : f(x) = {:{(sin^-1 |x|, x ne 0), (0, x = 0):} at x = 0

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Examine the function, f(x) = {{:(x - 1",",x lt 0),(1//4",",x = 0),(x^(...

    Text Solution

    |

  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

    Text Solution

    |

  3. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

    Text Solution

    |

  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

    Text Solution

    |

  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

    Text Solution

    |

  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

    Text Solution

    |

  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

    Text Solution

    |

  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |