# Find the domain of the function. f(x)= 2x^2+5x+3/2x^2-5x-3

### Solution:

First, let’s plot f(x) =

Here’s what the graph looks like:

Now, the definition of “domain of a function” as follows: The domain of a given function is the set of “input” values for which the function is defined.” For instance, the domain of cosine would be all real numbers, while the domain of the square root would be only numbers greater than or equal to 0 (ignoring complex numbers in both bases).

As you can see from the above graph, the function is valid for all “real” values of x, except for 0. The set of “real numbers”, as you may know, can be thought of as points on an infinitely long number line. The shorthand way of saying “all real numbers except for x” is as follows:

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