Precalculus Examples

$f g$ , $f (x) = \frac{x}{x + 1}$ , $g (x) = \sin (2 x)$

Step 1

Replace the function designators in $f g$ with the actual functions.

$(\frac{x}{x + 1}) (\sin (2 x))$

Step 2

Set the denominator in $\frac{x}{x + 1}$ equal to $0$ to find where the expression is undefined.

$x + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 1) \cup (- 1, \infty)$

Set-Builder Notation:

${x | x \neq - 1}$

Step 5