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

[brandon26]

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

 

[TD]

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.

 

[quicknote]

Sure, I'd be happy to explain how to calculate the inverse function of a given function. In this case, the given function is f(x)=2e^2x + 4.

To find the inverse function, we first need to switch the roles of x and y in the equation. This means that we will have y=2e^2x + 4 instead of x=2e^2y + 4.

Next, we need to isolate y on one side of the equation. In this case, we can subtract 4 from both sides to get y-4=2e^2x.

Then, we can divide both sides by 2e^2 to get y-4/2e^2=x.

Now, we have the inverse function in the form of y=f^-1(x) and we can replace y with f^-1(x) to get f^-1(x)=(x-4)/2e^2.

This is the inverse function of f(x)=2e^2x + 4. To check if this is correct, we can plug in a value for x and see if we get the original value of y.

For example, if we plug in x=2, we get f^-1(2)=(2-4)/2e^2=-2/2e^2=-1/e^2. And if we plug in y=-1/e^2 into the original function, we get f(-1/e^2)=2e^2(-1/e^2)+4=2-4=-2, which is the original value of y.

Therefore, we have successfully calculated the inverse function of f(x)=2e^2x + 4 to be f^-1(x)=(x-4)/2e^2. I hope this explanation helps!