Question

What is the domain of (cd)(x)?

Answer 1

we are given

$c(x)=\frac{3}{x-2}$

$d(x)=x+2$

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):

$c(x)=\frac{3}{x-2}$

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):

$d(x)=x+3$

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):

$c(x)=\frac{3}{x-2}$

$d(x)=x+3$

$(cd)(x)=c(x)*d(x)$

$(cd)(x)=\frac{3}{x-2}*(x+3)$

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