How to find domain and range of f(x)=x??

Question

my teacher made this problem up i think and it says explain your answer to get 100.

WTF?? what is the number

Answer 1

The domain of a function is just the set of x values which can be plugged in to the function to get a well-defined output.  For any real number x, f(x) = x outputs a well-defined number (specifically, x itself), so the domain of f(x) = x is (-infinity, infinity), or in other words, all real numbers.

The range of a function is just the set of f(x) values which can be obtained when all x values in the domain are plugged into f(x).  Any real number a can be obtained as the output of the function f(x) = x by just letting x = a, so the range of this function is also (-infinity, infinity), or all real numbers.

As an exercise, what are the domain and range of:

g(x) = x^2?

h(x) = sqrt(x)?