calculus multi variable

Question

Suppose f ,g , and h are functions of a single variable with domains ( − ∞ , 1 ) ,[ 0 , π ] , and ( − 1 , 1 ) , respectively. What is the domain of the function F ( x , y ) = f ( x ) − g ( x ) h ( y ) ?

Answer 1

A little note that I didn't think about when I recorded this: you can find the domain of this type of multivariable function by simply finding the intersection of the domains of all functions defined on x, then the intersection of the domains of all functions defined on y and that gives you the domain of the multivariable function. However, this only applies when the component functions are added, subtracted, or multiplied. You have to be careful if one of the functions is dividing another. In that case, you would additionally consider when and if that function was equal to zero and remove that value from the domain.