Question

If (x)=
X-2
and d(x) = x + 3, what is the domain of (cd)(x)?

Answer 1

Option (2)

Explanation:

Given functions are,

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

d(x) = x + 3

Equation of the composite function will be,

(cd)(x) = c(x) × d(x)

=
`(5)/((x-2))* (x+3)`

=
`(5(x+3))/((x-2))`

This function is defined only when denominator is not equal to zero.

(x - 2) ≠ 2

Therefore, for real numbers except x = 2 will be the domain of the composite function.

Option (2) will be the answer.