A function that is both One to One and Onto is called Bijective function. Below is a visual description of Definition 12.4. In mathematics, a bijective function or bijection is a function f : A → B that is both an injection and a surjection. If it crosses more than once it is still a valid curve, but is not a function. Each value of the output set is connected to the input set, and each output value is connected to only one input value. And I can write such that, like that. A function f : A -> B is said to be onto function if the range of f is equal to the co-domain of f. How to Prove a Function is Bijective without Using Arrow Diagram ? A function is invertible if and only if it is a bijection. Definition: A function is bijective if it is both injective and surjective. Question 1 : A bijective function is both injective and surjective, thus it is (at the very least) injective. My examples have just a few values, but functions usually work on sets with infinitely many elements. 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]. 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. Stated in concise mathematical notation, a function f: X → Y is bijective if and only if it satisfies the condition for every y in Y there is a unique x in X with y = f(x). 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). 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).. 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