Question

Help me understand if this is true: "for a one-to-one function y=f(x) then x=f^-1(y)."
And what would make it different in the case of "for any function y=f(x) then x=f^-1(y)"

Answer 1

yes for example

y = x^2 then x = +-sqrt(y)
but thats not a function by definition because any input must only have 1 ouput

Answer 2

So, would that then be true for a one-to-one function because it creates an inverse to the original function no matter what? But is it still true for a function that is not one-to-one? In example, a trigonometric function? @dumbcow

Answer 3

it is true for all one-to-one functions.

it is not true for functions that are not one-to-one

for these functions, you must restrict the domain to get the inverse function

Answer 4

so for example...
y = sin(x) the inverse is defined if you restrict the domain to -pi/2 <x<pi/2
for that section it acts like a one-to-one function

Answer 5

Thank you so much!