It is indeed false.
[tex]\sin^{-1}x[/tex] is a function that takes values of [tex]x[/tex] between -1 and 1, and takes on values between -π/2 and π/2. Most importantly, it's a function that takes *one* value in its domain and assigns it to exactly *one* value in its range. Hence [tex]\sin^{-1}x[/tex] is one-to-one.
It's true that [tex]\sin x=\frac45[/tex] has infinitely many solutions, but [tex]\sin x[/tex] itself is not one-to-one.
