C(x) = [tex]\frac{5}{x-2}[/tex]
d(x) = x+3
(cd)(x) = c(x) * d(x)
Replace c(x) and d(x) in the above expression
(cd)(x) =[tex]\frac{5}{x-2} * (x+3)[/tex]
(cd)(x) = [tex]\frac{5(x+3)}{x-2}[/tex]
Domain are the x values where function is defined
When denominator becomes 0 then function becomes undefined
To find domain we set the denominator =0 and solve for x
x - 2=0
x= 2
x=2 makes the denominator 0. Hence, domain is set of all real numbers except 2
Answer : all real values of x except 2
