how can i find out if the functions have and inverse function, given Df?

[blink]

how can i find out if the functions have an inverse function, given Df?
a) f(x) = x tan ((pi*x)/2) , D(f) = (−1, 1);
b) f(x) = x tan ((pi*x)/2), D(f) = [0, 1);

cant show my work since my brain melts down every time i look at this.
for me this is new, in only know how to find inverse of function when i got f.ex y=3x-2 ....

 

[stapel]

how can i find out if the functions have and inverse function, given Df?

How can you find out if the functions have what (and then figure out if they have an inverse function)? What is your book's definition of "Df"?

a) f(x) = x tan ((pi*x)/2) , D(f) = (−1, 1);
b) f(x) = x tan ((pi*x)/2), D(f) = [0, 1);

cant show my work since my brain melts down every time i look at this.
for me this is new, in only know how to find inverse of function when i got f.ex y=3x-2 ....

When you reply, please specify, as best you can figure out, how this exercise relates to, or uses the techniques of, calculus. Thank you!

 

[blink]

if the function have an inverse function. i dont think i have to calculate the inverse function, but that im supposed to ''see'' if it has one using the D(f).

 

[HallsofIvy]

I presume that by "D(f)" you mean "the domain of f". To have an inverse a function must be "one to one" on its domain. That is, if f(x)= f(y) then y= x.