Question 198279
# 1


{{{f(x) = x/(x + 3)}}} Start with the given function.



{{{f(x)f(x) = f(x)(x/(x + 3))}}} Multiply both sides by f(x).



{{{f(x)f(x) = (x/(x + 3))(x/(x + 3))}}} Plug in {{{f(x) = x/(x + 3)}}}



{{{f(x)f(x) = (x^2)/((x + 3)(x + 3))}}} Multiply



Take note that {{{x<>-3}}} since this causes a division by zero. So the domain is x can be any real number BUT x cannot equal -3.




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# 2


{{{g(x)=2x-3}}} Start with the given function.



{{{g(x)g(x)=g(x)(2x-3)}}} Multiply both sides by g(x).



{{{g(x)g(x)=(2x-3)(2x-3)}}} Plug in {{{g(x)=2x-3}}}



{{{g(x)g(x)=(2x)(2x)+(2x)(-3)+(-3)(2x)+(-3)(-3)}}} FOIL



{{{g(x)g(x)=4x^2-6x-6x+9}}} Multiply



{{{g(x)g(x)=4x^2-12x+9}}} Combine like terms.



Take note that there are no division by variables or square roots, logs, etc.. that would cause a division by zero or any other undefined property. So we don't need to worry about any restrictions.


So the domain is all real numbers.