Can 2 inputs have the same output in a function?

Each input has only one output. Remember that in a function, the input value must have one and only one value for the output. Domain and Range. There is a name for the set of input values and another name for the set of output values for a function.

Can two different functions have the same graph?

By definition, if having the same graph implies identical values of target values of identical range values, and if both functions have the same range – these two functions are actually a single function having two different names. No. They cannot.

What does it mean when two functions have the same domain?

equal
Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.

When two inputs give the same output it is known as?

2 Answers. You are correct. This is called a hash collision, and it’s a real thing.

Can the same function be represented by different formulas?

But as you note, if two different formulas for the right hand side actually give the same values when you substitute values from the domain, then the functions so defined will be the same. (,) is a binary operation on functions; it’s defining property is (g,h)(x)=(g(x),h(x)).

How do you prove that two functions are different?

So, if two functions have different codomains (e.g. R and C in your example), then they are different functions, even if they have the same graph. The other convention is to identify the function with its graph, so that any set f of ordered pairs (x,y) such that y1=y2 whenever (x,y1)∈f and (x,y2)∈f is a function.

How can two functions be the same?

The set A is called the domain of f and the set B is called the codomain. We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a). We often write f:A→B to indicate that f is a function from A to B.

Can two inputs have the same output hash?

If two separate inputs produce the same hash output, it is called a collision. This collision can then be exploited by any application that compares two hashes together – such as password hashes, file integrity checks, etc. For example, let’s say we have a hypothetical hash function.