Home
Class 12
MATHS
If f(x) = x + tan x and f is the inverse...

If `f(x) = x + tan x` and `f` is the inverse of `g`, then `g'(x)` is equal to

A

`(1)/(1+[g(x)-x]^(2))`

B

`(1)/(2-[g(x)-x]^(2))`

C

`(1)/(2+[x-g(x)]^(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x+tan x`
`therefore" "f(f^(-1)(y))=f^(-1)(y)+tan f^(-1)(y)`
`"or "y=g(y)+tan g(y)`
`"or "x=g(x)+tan g(x)`
Differentiating, we get `1=g'(x)+sec^(2)g(x)g'(X)`
`"or "g'(x)=(1)/(1+sec^(2)g(x))=(1)/(2+[g(x)-x]^(2))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

If f(x)=x+tanx and g(x) is the inverse of f(x), then differentiation of g(x) is (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)+x]^2) (c) 1/(2+[g(x)-x]^2) (d) none of these

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals

Let f(x)=x^(x),x in (0,oo) and let g(x) be inverse of f(x), then g'(x) must be

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i equal to :

Let f:R to R be defined by f(x)=x^(2) and g:R to R be defined by g(x)=x+5 . Then , (gof)(x) is equal to -

Let f(x) be a polynomial of degree one and f(x) be a function defined by f(x)={(g(x), x le0), ((1+x)/(2+x)^(1//x), x gt0):} If f(x) is continuous at x=0 and f(-1)=f'(1), then g(x) is equal to :

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and given that f(5)=5, then f(10) is equal to

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(...

    Text Solution

    |

  2. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  3. If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to

    Text Solution

    |

  4. If g is the inverse of a function f and f ' ( x ) = 1 / (1 + x^...

    Text Solution

    |

  5. If y = ((sin^ (−1) x)) , prove that ( 1 − x^ 2 ) d 2 y d x 2 − x...

    Text Solution

    |

  6. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

    Text Solution

    |

  7. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b...

    Text Solution

    |

  8. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  9. answeer the following : (i) if y sqrt(x^2+1)=log(sqrt(x^2+1)-x), show ...

    Text Solution

    |

  10. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  11. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

    Text Solution

    |

  12. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  13. If y=x^((x^(x))) then (dy)/(dx) is

    Text Solution

    |

  14. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

    Text Solution

    |

  15. Let f(x)=x^(x),x in (0,oo) and let g(x) be inverse of f(x), then g'(x)...

    Text Solution

    |

  16. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

    Text Solution

    |

  17. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

    Text Solution

    |

  18. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f^(prime prime)(x...

    Text Solution

    |

  19. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

    Text Solution

    |

  20. (d^n)/(dx^n)(logx)=? (a)((n-1)!)/(x^n) (b) (n !)/(x^n) (c)((n-2)!)/(...

    Text Solution

    |