we are given
[tex]c(x)=\frac{3}{x-2}[/tex]
[tex]d(x)=x+2[/tex]
Firstly, we will find domain of c(x) , d(x) and then (cd)(x)
and then we can find common domain
Domain of c(x):
[tex]c(x)=\frac{3}{x-2}[/tex]
we know that domain is all possible values of x for which domain is defined
we know that any function is undefined when denominator =0
x-2=0
x=2
so, domain of c(x) is all values of x except at x=2
Domain of d(x):
[tex]d(x)=x+3[/tex]
we know that domain is all possible values of x for which domain is defined
we know that any function is undefined when denominator =0
we don't have denominator here
so, domain of d(x) is all real values of x
Domain of (cd)(x):
[tex]c(x)=\frac{3}{x-2}[/tex]
[tex]d(x)=x+3[/tex]
[tex](cd)(x)=c(x)*d(x)[/tex]
[tex](cd)(x)=\frac{3}{x-2}*(x+3)[/tex]
we know that domain is all possible values of x for which domain is defined
we know that any function is undefined when denominator =0
x-2=0
x=2
so, domain of c(x) is all values of x except at x=2
so, common domain is all real values of x except at x=2
so, option-B........Answer
