If you can graph this, find the inverse of this function.
Hi,
thank you for asking this question! As a Math AA HL student, although there are various ways that I can solve this question, I recommend you to use a FANTASTIC Graphing Calculator called “Desmos.” If you have any math questions, use this website!
If you look at the graph, the y-intercept is (0,3) and the minimum point is (2.101, 0.583). Since it is not a one-to-one function that passes horizontal line test, we should set the domain to figure out the inverse function of the original function y=(x^2 - 4x + 6)/(x^0.5 + 2).
In the first case, when x is greater than or equal to 2.101, we switch x and y in the original function. We also switch the domain restriction in the original function into range restriction in the inverse function.
In the second case, when x is smaller than 2.101, through the same process, the inverse function can be drawn below:
If you know that inverse functions only exist when the original function is a one-to-one function and the domain and range must be switched, you can easily figure out the inverse function of most of the functions.
Hope this helps!
Dear Letterbox