Help with domains of functions?

Question

jango_in_dtown · Answer

find the roots of the equation g(x)=0

jango_in_dtown · Answer

at those points the function f/g will not be defined and hence the domain will be the set of real numbers except those two points

jango_in_dtown · Answer

ok... so see any number divided by 0 is undefined right?

jango_in_dtown · Answer

in the same way, any function divided by 0 will be undefined..

jango_in_dtown · Answer

here you have f/g.. so g must not be zero

jango_in_dtown · Answer

thus solve for g(x)=0 then.. i.e. x^2 -4x +3=0

mathmale · Answer

The 'domain' of a function is the SET OF NUMBERS that are acceptable inputs.  

Looking at your "Find the domain of the function where (f divided by g) (x)  where f(x)=x^2-9  and g(x)= x^2 -4x +3,"  or$$(f/g)(x)=\frac{ x^2-9 }{ x^2-4x+3}$$

mathmale · Answer

and realizing that division by zero is undefined, purposely set the denom. = to 0 and solve for x.  Results:  {1, 3}.  These two solutions are NOT part of the domain of this function.  In positive terms, you could state that "the domain is the set of all real numbers of that 1 or 3."  Or you could use set notation:  (-inf, 1), (1, 3), (3, inf.)

mathmale · Answer

That's what I said earlier.  Division by zero is not allowed, so purposely set the denominator (not "bottom part") equal to zero and solve the resulting equationf or x.  And so on.