Posted by T.Gracken on August 12, 2002 at 09:53:56:
In Reply to: Inverse Functions posted by JohnMayer on August 12, 2002 at 01:27:02:
: In the exercise we had to determine whether the given funtion had an inverse or not (and if so, we had to give the domain and range of the inverse and graph the function and its inverse... so far i've had no trouble, except when i hit problem #11... i thought it had an inverse, but it doesn't... why is that? (Here's the QUesTion:
: 11. f(z) = tan z
: ... btw, how would you handle a problem with a sin and x (#8- f(x) = x + sinx ... [ i just grapghed it and inversed it... but is that incorrect?])
first of all, EVERY function has an inverse.
Now, if you mean "determine whether the function has an inverse function", that is another matter [i.e. is the inverse of a function also a function?]. A function has an inverse function if and only if the function is one to one. Since the tangent function is not one to one, it does not have an inverse function. However, if you restrict the domain of the tangent function, it is possible for it to have an inverse function.
as far as "I just grapghed it and inversed it..."; that makes no sense what-so-ever!