Home
Class 11
MATHS
The function f(x)=e^x+x , being differe...

The function `f(x)=e^x+x ,` being differentiable and one-to-one, has a differentiable inverse `f^(-1)(x)dot` The value of `d/(dx)(f^(-1))` at the point `f(log2)` is (a)`1/(1n2)` (b) `1/3` (c) `1/4` (d) none of these

A

`(1)/(In2)`

B

`(1)/(3)`

C

`(1)/(4)`

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the derivative of the inverse function \( f^{-1}(x) \) at the point \( f(\log 2) \). The function given is \( f(x) = e^x + x \). ### Step-by-Step Solution: 1. **Define the Function and Its Inverse**: We have the function: \[ f(x) = e^x + x ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The function f(x)=e^(x)+x, being differentiable and one- to -one, has a differentiable inverse f^(-1)(x). The value of (x)/(dx)(f^(-1)at f(log2) is

If f(x)=|x|+|x-1|, write the value of (d)/(dx)f(f(x))

Let f(x)=x^(5)+2x^(3)+3x+4 then the value of 28(d)/(dx)(f^(-1)) at x=-2 is

Let f(x) be a differentiable and let c a be a constant.Then cf(x) is also differentiable such that (d)/(dx){cf(x)}=c(d)/(dx)(f(x))

If adifferentiabl e function f(x)=e^(x)+2x is given,then equal to (d)/(dx)(f^(-1)(x)) at x=f(ln3) is equal to

Let f:R rarr R be a one-one onto differentiable function,such that f(2)=1 and f'(2)=3. The find the value of ((d)/(dx)(f^(-1)(x)))_(x=1)

If f(x)=x+1, then write the value of (d)/(dx)(fof)(x)

If (d)/(dx)(f(x))=4x such that f(2)=0, then f(x) is

The value of (d)/(dx)(f^(-1)(x)) at x=9 for f(x)=x^(3)-2x^(-3)-3+10 is (x>0) (A) -(1)/(3)(B)(1)/(9)(C)(1)/(27) (D) none

Let a continous and differentiable function f(x) is such that f(x) and (d)/(dx)f(x) have opposite signs everywhere. Then,