Precalculus Examples

If $c (x) = \frac{5}{x - 2}$ and $d (x) = x + 3$ ; what is the domain of $(c d) (x)$ ?

Step 1

Evaluate $c d$ .

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Step 1.1

Replace the function designators in $c d$ with the actual functions.

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

Step 1.2

Multiply $\frac{5}{x - 2}$ by $x + 3$ .

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

Step 2

Evaluate $c d$ at $x$ .

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

Step 3

Simplify $\frac{5 ((x) + 3)}{(x) - 2}$ .

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Step 3.1

Remove parentheses.

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

Step 3.2

Remove parentheses.

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