$$ Now this function is bijective and can be inverted. Below is a visual description of Definition 12.4. Infinitely Many. The function f is called as one to one and onto or a bijective function, if f is both a one to one and an onto function. More clearly, f maps distinct elements of A into distinct images in B and every element in B is an image of some element in A. Thus, if you tell me that a function is bijective, I know that every element in B is “hit” by some element in A (due to surjectivity), and that it is “hit” by only one element in A (due to injectivity). Functions that have inverse functions are said to be invertible. If it crosses more than once it is still a valid curve, but is not a function. In essence, injective means that unequal elements in A always get sent to unequal elements in B. Surjective means that every element of B has an arrow pointing to it, that is, it equals f(a) for some a in the domain of f. Hence every bijection is invertible. Definition: A function is bijective if it is both injective and surjective. The inverse is conventionally called $\arcsin$. This is equivalent to the following statement: for every element b in the codomain B, there is exactly one element a in the domain A such that f(a)=b.Another name for bijection is 1-1 correspondence (read "one-to-one correspondence).. So we can calculate the range of the sine function, namely the interval $[-1, 1]$, and then define a third function: $$ \sin^*: \big[-\frac{\pi}{2}, \frac{\pi}{2}\big] \to [-1, 1]. A function that is both One to One and Onto is called Bijective function. Question 1 : In mathematics, a bijective function or bijection is a function f : A → B that is both an injection and a surjection. Some types of functions have stricter rules, to find out more you can read Injective, Surjective and Bijective. 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