0
votes
1answer
34 views

Following flash, a camera's battery begins to recharge the flash’s capacitor, which stores electric charge given by $Q(t) = Q_0(1 − e^{−t/a})$

(The maximum charge capacity is $Q_0$ and $t$ is measured in seconds). (a) Find the inverse of this function and explain its meaning. (b) How long does it take to recharge the capacitor to 90% of ...
0
votes
1answer
21 views

How to find the inverse of a function involving e with a coefficient?

I was wondering how I would find the inverse of the following function, since the e has a co-efficient: $\frac{e^x}{1+2e^x}=y$ I got as far as $\ln y+\ln(2e^x) = \ln e^x$, which would be changed ...
2
votes
3answers
39 views

inverse of quadratic log functions

Can a Log function with a quadratic have an inverse function? The specific question is to find the inverse of $$f(x) = \log_2(x^2-3x-4)$$ The function already fails the horizontal line test, but ...
0
votes
2answers
24 views

Find the inverse of the function

Find the inverse of the function $f(x) = -2 \cdot4^{2(x-3)} - 1$.
1
vote
2answers
24 views

How do I find the inverse of this exponential function?

$x=-3(3^{-x})+9$ I know the steps up until a certain point. $x=-3(3^{-y})+9$ $x-9=-3(3^{-y})$ $\frac{(x-9)}{-3} = 3^y$ $ln (\frac{x-9}{-3}) = -y * ln 3$ Not sure what to do from here. I know I ...
1
vote
1answer
36 views

Find the inverse function about a exponential related function

Here is the function:$$y = 4x + {x^m},where{\text{ 0 < m}} \leqslant {\text{1;}}$$ Approximately results is acceptable.
0
votes
4answers
71 views

$f:\mathbb R \to (0,\infty)$ defined by $f(x)=e^x$. Describe its inverse.

How do I go about describing it? Well first is the inverse $e^{-x}$ or $\ln(x)$? Additionally, since I have no clue how to solve these problems as I am probably overthinking them... $f:\mathbb R\to ...
3
votes
2answers
77 views

Why is $3^n$ not in $\Theta(2^n)$

How is it that $3^n$ not in $\Theta(2^n)$, while $log_3 n$ is in $\Theta(log_2 n)$ ?
0
votes
1answer
44 views

differentiate of an inverse function of mixed exponential and algebraic form

Let $f(x)= e^{2x} + x^5 + 1$ Find $(f^{-1})'(2)$ Find $(f^{-1})''(2)$ There is a missing link in my brain with regards to dealing with a function containing exponential and algebra. :/ I'm ...
0
votes
2answers
40 views

Solving inverse of function

Given: $f(t)=500(1.1)^t$ How would I mathmatically solve for: $f^{-1}(3000)$
2
votes
1answer
94 views

Derivative of the inverse of $y=(a+bx)e^{cx}$

I need to solve for the 1st derivative of the inverse of $y=(a+bx)e^{cx}$ but my calculus is a bit rusty. I know that to get the inverse function, I would have to use the Lambert W method but I think ...
1
vote
2answers
131 views

inverse of laplace transform

How to compute this inverse Laplace transform ? $$\displaystyle{ \mathcal{L^{-1}} \left\{ \frac{1}{s(\exp(s)+1)} \right\} }$$ Thanks.
5
votes
2answers
718 views

Help finding inverse of $f(x)=\frac{e^x-e^{-x}}{2}$

I'm trying to find the inverse of $f(x)=\frac{e^x-e^{-x}}{2}$. My textbook says $f^{-1}(x)=\ln(x+\sqrt{x^2+1})$, but I haven't been able to get that answer. Switching $x$ and $y$, I tried solving for ...
3
votes
3answers
6k views

The relation between an exponential function and a logarithmic function

I have been told multiple times that the logarithmic function is the inverse of the exponential function and vice versa. My question is; what are the implications of this? How can we see that they're ...
4
votes
2answers
151 views

Solve equation $\tfrac 1x (e^x-1) = \alpha$

I have the equation $\tfrac 1x (e^x-1) = \alpha$ for an positive $\alpha \in \mathbb{R}^+$ which I want to solve for $x\in \mathbb R$ (most of all I am interested in the solution $x > 0$ for ...
4
votes
2answers
119 views

$\ln(x)$, $e^{x}$ and $\int \frac{1}{x}dx$ relationship

My math professor told me that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ by the definition; so far so good. But how/why does $\ln(x)$ ($\int_1^x\frac{1}{t} dt$: by defintion) coincide with the inverse of ...