Home
Class 12
MATHS
Q. f={(x+a if x<0), (|x-1| if x>=0) g(...

Q. f={`(x+a if x<0)`, `(|x-1| if x>=0)` `g(x)={(x+1 if x<0),(x-1)^2 + b if x>=0)` where a and b are non-negative real numbers. Determine the composite function `gof`. If `(gof)(x)` is continuous for all real x, determine the values of a and b, Further for these values of a and b, is `gof` differentiable at x=0? Justify your answer.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL -1|134 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(x^3+x^2-16x+20)/(x-2)^2,x ne 0 k, x=0 is continuous for all real values of x, find the value of K.

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

Determine the values of a ,\ b ,\ c for which the function f(x)={(sin(a+1)x+sinx)/x , for x 0 is continuous at x=0

Determine the values of a , b , c for which the function f(x)={((sin(a+1)x+sinx)/(x ) ,, x 0):} is continuous at x=0

Find the least value of f(x)=a x+b/x , where a >0,\ \ b >0 and x >0 .

If f(a+b+1-x)=f(x) , for all x where a and b are fixed positive real numbers, the (1)/(a+b) int_(a)^(b) x(f(x)+f(x+1) dx is equal to :

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

If f(x)=sqrt(1-x) and g(x)=(log)_e x are two real functions, then describe functions fog and gof .

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL 2
  1. Suppose f and g are two functions such that f,g: R ->R f(x)=ln(1+sqrt(...

    Text Solution

    |

  2. If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x)...

    Text Solution

    |

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

    Text Solution

    |

  4. If f(x)=-1+|x-2|,0lexle4 g(x)=2-|x|,-1lexle3 Then find fog(x) and ...

    Text Solution

    |

  5. Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If f(...

    Text Solution

    |

  6. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  7. Let f(x) = sqrt(x - 1)+sqrt(x+ 24 - 10sqrt(x-1)), 1 lt x lt 26 be a re...

    Text Solution

    |

  8. If f(x)=(|x|)^(|sinx|), then f'(-pi//4) is equal to

    Text Solution

    |

  9. If f(x) = cos x cos 2x cos 4x cos 8x cos 16x then find f' (pi/4)

    Text Solution

    |

  10. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  11. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  12. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  13. underset(xto0)lim[(1-e^(x))(sinx)/(|x|)] is (where [.] represents the ...

    Text Solution

    |

  14. Indicate all correct alternatives: if f(x) = x/2-1, then on the interv...

    Text Solution

    |

  15. Let function f be defined as f:R^(+)toR^(+) and function g is defined ...

    Text Solution

    |

  16. If f(x)={(2cos x ,s in2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x...

    Text Solution

    |

  17. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  18. Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is different...

    Text Solution

    |

  19. {:(f(x) = cos x and H(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)...

    Text Solution

    |

  20. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |