Calculating Inverse Functions: Example f(x)=2e^2x + 4

AI Thread Summary
To find the inverse of the function f(x) = 2e^(2x) + 4, first switch the roles of x and y, resulting in x = 2e^(2y) + 4. Next, isolate the exponential term by subtracting 4 from both sides, yielding x - 4 = 2e^(2y). Then, divide by 2 to get (x - 4)/2 = e^(2y). Finally, take the natural logarithm of both sides and solve for y, resulting in y = (1/2)ln((x - 4)/2). Thus, the inverse function is f^(-1)(x) = (1/2)ln((x - 4)/2).
brandon26
Messages
107
Reaction score
0
Could someone please explain to me how to work out the inverse function of a function?
Please use the format f(x)=2e^2x + 4 as an example, if possible.
thanks
 
Physics news on Phys.org
brandon26 said:
Could someone please explain to me how to work out the inverse function of a function?
Please use the format f(x)=2e^2x + 4 as an example, if possible.
thanks
Try switching the roles of x and y and solve for y again, where f(x) = y of course.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

I What are the applications of inverses of vector functions?
Replies
17
Views
3K
Composite and Inverse Functions Problem
Replies
3
Views
2K
Intensity of Stars and the Inverse Square Law Problem
Replies
10
Views
3K
I Local inverse of non bijective functions
Replies
9
Views
3K
MHB Prove f is One-to-One: (a) and (b) | Help with Choosing Inverse Formula
Replies
2
Views
2K
State the domain and range for a given function
Replies
7
Views
2K
Find the inverse function of ##f(x) =x^4+2x^2##
Replies
11
Views
3K
I want to see the plot of an inverse function -- can I use a TI84?
Replies
10
Views
6K
Can this function still be a constant function?
Replies
11
Views
1K
To find the range of a given ##\sin## function
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top