Algebra Examples

$f (x) = \frac{6}{x + 8}$ , $g (x) = x + 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 1)$ by substituting in the value of $g$ into $f$ .

$f (x + 1) = \frac{6}{(x + 1) + 8}$

Step 3

Set the denominator in $\frac{6}{(x + 1) + 8}$ equal to $0$ to find where the expression is undefined.

$(x + 1) + 8 = 0$

Step 4

Solve for $x$ .

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Step 4.1

Add $1$ and $8$ .

$x + 9 = 0$

Step 4.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 5

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

Interval Notation:

$(- \infty, - 9) \cup (- 9, \infty)$

Set-Builder Notation:

${x | x \neq - 9}$

Step 6