Example 1: The function f (x) = x2 from the set of positive real numbers to positive real numbers is injective as well as surjective. Thus, it is also bijective. However, the same function from the set of all real numbers R is not bijective since we also have theRead More →
Examples of Injective Function If function f: R→ R, then f(x) = 2x is injective. If function f: R→ R, then f(x) = 2x+1 is injective. If function f: R→ R, then f(x) = x2 is not an injective function, because here if x = -1, then f(-1) = 1Read More →
A continuous, injective function f:R→R is either strictly increasing or strictly decreasing. I would like to prove the statement in the title. Proof: We prove that if f is not strictly decreasing, then it must be strictly increasing. Which function is always bijective? A function f: R → R isRead More →
Not all functions have inverse functions. Those that do are called invertible. For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y. How do you proveRead More →