Home
Class 12
MATHS
If f(x)=|x-2| and g(x)=f[f(x)], then g'(...

If `f(x)=|x-2|` and `g(x)=f[f(x)]`, then `g'(x)=`………… for `x gt20`.

A

1

B

2

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
For `x gt 20`, we have
`f(x)=x-2`
`Rightarrow g(x)=f(f(x))=f(x-2)=(x-2)=x-4`
`Rightarrow g'(x)=1"for "x gt 20`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

If f(x)=|x-2|" and "g(x)=f(f(x)), then for xgt20,g'(x) equals

If f(g(x))=4x^(2)-8x and f(x)=x^(2)-4, then g(x)=

If f(x)=|x-2|" and "g(x)=f(f(x)), then for 2ltxlt4,g'(x) equals

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

If f(x) = x log x and g(x) = 10^(x) , then g(f(2)) =

If f(x) =4x^2 and g(x) =f(sin x)+f(cos x), then g (23^(@)) is

If f(x)=e^(x) and g(x)=f(x)+f^(-1) , what does g(2) equal?

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then f(x)=sin^2x ,g(x)=sqrt(x) f(x)=sinx ,g(x)=|x| f(x=x^2,g(x)=sinsqrt(x) fa n dg cannot be determined

OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Section I - Solved Mcqs
  1. If the function f(x) is given by f(x)={{:(,2^(1//(x-1)),x lt 1),(,ax^(...

    Text Solution

    |

  2. Let f(x)=sin x,g(x)=[x+1] and h(x)=gof(x) where [.] the greatest integ...

    Text Solution

    |

  3. If f(x)=|x-2| and g(x)=f[f(x)], then g'(x)=………… for x gt20.

    Text Solution

    |

  4. If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)),then at x=0,g(x)...

    Text Solution

    |

  5. Let f(x)=cos x and g(x)=[x+1],"where [.] denotes the greatest integer ...

    Text Solution

    |

  6. f(x)=min{1,cosx,1-sinx},-pilexlepi, then

    Text Solution

    |

  7. If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)...

    Text Solution

    |

  8. If f(x) = sgn(x^5), then which of the following is/are false (where sg...

    Text Solution

    |

  9. If f (x) =|x-1|and g (x) =f (f (f (x))), then g' (x) is equal to:

    Text Solution

    |

  10. If f(x)={{:(,(1)/(x)-(2)/(e^(2x)-1),x ne 0),(,1,x=0):}

    Text Solution

    |

  11. Let f(x)=(-1)^([x^(3)]), where [.] denotest the greatest integer funct...

    Text Solution

    |

  12. f(x)=(1)/(1-x)and f^(n)=fofof....of, then the points of discontinuitym...

    Text Solution

    |

  13. Let f(x) = [ n + p sin x], x in (0,pi), n in Z, p is a prime number an...

    Text Solution

    |

  14. Determine the values of x for which the following functions fails to b...

    Text Solution

    |

  15. Let [x] denote the greatest integer less than or equal to x and g (x) ...

    Text Solution

    |

  16. Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):},...

    Text Solution

    |

  17. Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x)...

    Text Solution

    |

  18. Let f(x) be a continuous defined for 1le xle 3. if f(x) takes ra...

    Text Solution

    |

  19. Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) ...

    Text Solution

    |

  20. If f(x) is periodic function with period, T, then

    Text Solution

    |