╔(σ_σ)╝ said:Have you considered finding g(e) ?
When i looked at g i knew that the x^2 term would cause problems. I looked again at g and realized there was a 2 infront of lnx and i knew ln(e) =1. From there i realized that if i found g(e) i would get 2. ;-)raptik said:Oh!
If I put x=e, then I get g(e) = 2. So (e,2). Then it's inverse is (2,e) which matches with g-1(2) to give me e. I see how that could work, but how did you have the intuition to add e to the original problem? I suppose it's a matter of plugging something that seems like it would give me the required value until it works. Thnx for help.
An inverse function is a function that "undoes" the original function. In other words, if we plug in the output of the original function into the inverse function, we will get back the input of the original function.
To solve for the inverse function, we can follow these steps:
The inverse function of g(x) is f-1(x) = ex - 2ln(x) + e.
To check if a function is its own inverse, we can plug in the function into itself and see if we get back the original input. In other words, if f(f(x)) = x, then the function is its own inverse.
The domain of the inverse function is the range of the original function, which is (0,∞). The range of the inverse function is the domain of the original function, which is (-∞,∞).