The function f(x) = e^x + x,being differentia | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = e^x + x$. We need to find $(f^{-1})'(f(\ln 2))$. By the formula for the derivative of an inverse function,$(f^{-1})'(y) = \frac{1}{f

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(B) Given $f(x) = e^x + x$. We need to find $(f^{-1})'(f(\ln 2))$. By the formula for the derivative of an inverse function,$(f^{-1})'(y) = \frac{1}{f'(x)}$,where $y = f(x)$. Here,$y = f(\ln 2)$,so $x = \ln 2$. First,find $f'(x)$: $f'(x) = \frac{d}{dx}(e^x + x) = e^x + 1$. Now,evaluate $f'(x)$ at $x = \ln 2$: $f'(\ln 2) = e^{\ln 2} + 1 = 2 + 1 = 3$. Therefore,$(f^{-1})'(f(\ln 2)) = \frac{1}{f'(\ln 2)} = \frac{1}{3}$.

The function $f(x) = e^x + x$,being differentiable and one-to-one,has a differentiable inverse $f^{-1}(x)$. The value of $(f^{-1})'(f(\ln 2))$ is

Similar Questions

If $f(x)$ and $g(x)$ are inverse functions of each other and $f(x) = x + e^x$, then $g'(x) = ...$

Which of the following functions is invertible?

State with reason whether the following function has an inverse: $f: \{1,2,3,4\} \rightarrow \{10\}$ with $f = \{(1,10), (2,10), (3,10), (4,10)\}$.

The number of integral values of $a$ for which the function $f: R \to R, f(x) = 2x^3 - 3(a + 2)x^2 + 12ax - 7$ where $a \in [-4, 6]$ is invertible,is

If $f: R \rightarrow R$ is a mapping defined by $f(x)=x^{3}+5$,then $f^{-1}(x)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module