top of page

How do we graph y = (x^2 - 4x + 6)/(x^0.5 + 2)?

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

Comments


bottom of page