Tagged Questions
5
votes
2answers
98 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 ...
1
vote
1answer
102 views
How would I create a exponential ramp function from 0,0 to 1,1 with a single value to explain curvature?
I need an exponential function that will take linear input from 0,0 to 1,1 and give me back an exponential shaped curve such that changes in X near the 0 point result in small increases in Y, but each ...
2
votes
3answers
257 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 ...
0
votes
1answer
194 views
Exponential and power functions through two points
I have a problem where I'm asked to determine the constants of exponential and power functions that go through both points (5, 50) and (10, 1600). I have tried to solve them below, but would ...
0
votes
1answer
80 views
How do I solve this exponential equation?
$$x = 2^{x-3}$$
Does there exist an analytical solution to this equation? If so, how do I find it?
What if it is changed to an equality?
$$x>2^{x-3}$$
2
votes
1answer
77 views
Reflecting an exponential function over a y = 3 line.
How would you write the equation of $f(x) = 4^x$ that reflects over the line $y = 3$?
I've put in $f(x) = 3 + 4^{-x}$ which I thought was the right answer, but it isn't.
Thanks in advance!
2
votes
2answers
79 views
Exponential growth function
Under ideal conditions a certain bacteria population is know to double every three hours. Suppose that there are initially 100 bacteria. How would you go about formulating a function for this?
