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If ( look at the picture ) and d(x) = x + 3, what is the domain of (cd)(x)?

-all real values of x
-all real values of x except x = 2
-all real values of x except x = –3
-all real values of x except x = 2 and x = –3

If look at the picture and dx x 3 what is the domain of cdx all real values of x all real values of x except x 2 all real values of x except x 3 all real values class=

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facundo3141592

Answer: Hi!

so you have [tex]c(x) =\frac{5}{2 - x}[/tex] and [tex]d(x) = x + 3[/tex]

The first thing you can notice is that the domain of c is all reals minus the number 2 (because the denominator is 0), and the domain of d is al the reals.

then [tex](cd)(x) = c(x)*d(x) = \frac{5x + 3}{2 - x}[/tex]

Again the only problem here is when x = 2, because the denominator is zero in that case, then the domain of (cd)(x) is al real values except x = 2, which is the second option

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