The inverse is conventionally called $\arcsin$. $$ Now this function is bijective and can be inverted. Question 1 : As pointed out by M. Winter, the converse is not true. A bijective function is both injective and surjective, thus it is (at the very least) injective. And a function is surjective or onto, if for every element in your co-domain-- so let me write it this way, if for every, let's say y, that is a member of my co-domain, there exists-- that's the little shorthand notation for exists --there exists at least one x that's a member of x, such that. So we can calculate the range of the sine function, namely the interval $[-1, 1]$, and then define a third function: $$ \sin^*: \big[-\frac{\pi}{2}, \frac{\pi}{2}\big] \to [-1, 1]. If it crosses more than once it is still a valid curve, but is not a function. Thus, if you tell me that a function is bijective, I know that every element in B is “hit” by some element in A (due to surjectivity), and that it is “hit” by only one element in A (due to injectivity). Definition: A function is bijective if it is both injective and surjective. In essence, injective means that unequal elements in A always get sent to unequal elements in B. Surjective means that every element of B has an arrow pointing to it, that is, it equals f(a) for some a in the domain of f. Some types of functions have stricter rules, to find out more you can read Injective, Surjective and Bijective. Below is a visual description of Definition 12.4. Functions that have inverse functions are said to be invertible. Infinitely Many. My examples have just a few values, but functions usually work on sets with infinitely many elements. Each value of the output set is connected to the input set, and each output value is connected to only one input value. 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