Question

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

Answer 1

Answer:

Option (2)

Step-by-step explanation:

Given functions are,

c(x) = $\frac{5}{x-2}$

d(x) = x + 3

Equation of the composite function will be,

(cd)(x) = c(x) × d(x)

          = $\frac{5}{(x-2)}\times (x+3)$

          = $\frac{5(x+3)}{(x-2)}$

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.