Question

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

Answer 1

we are given

`c(x)=(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)=(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)=(3)/(x-2)`

`d(x)=x+3`

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

`(cd)(x)=(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