Home
Class 12
MATHS
Let f(x) be difined in the interval [-2...

Let f(x) be difined in the interval [-2, 2] such that
`f(x)={{:(-1", " -2lexle0),(x-1", " 0ltxle2):}`
and `g(x)=f(|x|)+|f(x)|`.
Test the differentiability of g (x) in (-2, 2).

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos
  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| What is the value of differential coefficent of g(x) at x=-2

Let f(x) be defined on [-2,2[ such that f(x)={{:(,-1,-2 le x le 0),(,x-1,0 le x le 2):} and g(x)= f(|x|)+|f(x)| . Then g(x) is differentiable in the interval.

Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| What is the value of the differential coefficient of g(x) at x=-2?

Let f(x) be defined in the interval [-2,2] such that f(x)={-1;-2<=x<=0} and f(x)={x-1;0

Let f(x) be defined in the interval [-2,2] such that f(x)=-1 for -2<=x<0 and 1-x for 0<=x<2.g(x)=f(|x|)+|f(x)| The number of points where g(x) is not differentiable in (-2, 2),is

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

Consider f(x)={{:(-2",",-1lexlt0),(x^(2)-2",",0lexle2):} and g(x)=|f(x)|+f(|x|) . Then, in the interval (-2, 2), g(x) is

Let f(x) = {{:(-1,-2 le x lt 0),(x^2-1,0 le x le 2):} and g(x)=|f(x)|+f(|x|) . Then , in the interval (-2,2),g is

Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| Which of the following statement is correct ? g(x) is differentiable at x=0 g(x) is differentiable at x=2

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0, test the continuity & ...

    Text Solution

    |

  2. If f(x)= ax^2-b, |x|<1 and f(x)=-1/|x|, |x|>=1 is derivable at x=1 th...

    Text Solution

    |

  3. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

    Text Solution

    |

  4. Discuss the continuity and differentiability in 0,2] of f(x)={|2x-3|...

    Text Solution

    |

  5. Let a1 and a2 be two values of a for which f(x)= x*{ln(1+x)+ln(1-x)}/(...

    Text Solution

    |

  6. Discuss the continuity & the derivability of 'f' where f(x)= degree ...

    Text Solution

    |

  7. Consider the function f(x)=[x^2|cospi/(2x)|\ if\ x!=0 0,\ \ \ \ \ \ ...

    Text Solution

    |

  8. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  9. If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x...

    Text Solution

    |

  10. The integer ' n ' for which (lim)(xvec0)((cos x-1)(cos x-e^x))/(x^n) i...

    Text Solution

    |

  11. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

    Text Solution

    |

  12. Let f: Rvec be such that f(!)=3a n df^(prime)(1)=6. Then ("lim")(xvec...

    Text Solution

    |

  13. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

    Text Solution

    |

  14. If (lim)(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the val...

    Text Solution

    |

  15. If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...

    Text Solution

    |

  16. The function given by y=||x|-1| is differentiable for all real n...

    Text Solution

    |

  17. If |f(x1) - f(x2)| le (x1 - x2)^(2), AA x1 , x2 in R. Find the equatio...

    Text Solution

    |

  18. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  19. If lim(x-&gt;0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b &gt;0,where theta...

    Text Solution

    |

  20. If f(x) {-x-pi/2,xle-pi/2 and -cosx,-pi/2 < xle0 and x-1,0< x le1 and ...

    Text Solution

    |