All the wonder Brilliant users and all my followers, this day I am going to share something really very interesting and may be something new for many of you.
Inspired from a question by @Calvin Lin sir, I have got some discussion points in my mind.
Hope, you all are aware of functions (make mathematics awesome and easy). Here I would like to talk about the function itself and its inverse.
Inverse of a function will exist, if and only if it is one-one(injective) function and onto (surjective) function. Combining one-one and onto together, the function is called Bijective function.
There comes a property of inverse functions :
Graphs of and are symmetrical about the line and intersect on the line .
whenever graphs intersect.
Now here are some points (questions) :
So if we talk about and its inverse functions . How many points of intersection will be there ? The above property says that there will be only 1 solution of But algebraically two solutions So now the point is exactly how many roots are there for the equation
Is the above stated property wrong ?
Can there be functions for which has solutions except which lie on the line . If yes, then finite or infinite number ?
Why does the equation not follow the above property ?
Note: You can add more discussion points here and analyse it as much as you can.
Thank you !