Trigonometry Examples

f (x) = - 3 \ln (x - 4)

$f (x) = - 3 \ln (x - 4)$

Step 1

Set the argument in

\ln (x - 4)

$\ln (x - 4)$ greater than

0

$0$ to find where the expression is defined.

x - 4 > 0

$x - 4 > 0$

Step 2

Add

4

$4$ to both sides of the inequality.

x > 4

$x > 4$

Step 3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(4, \infty)

$(4, \infty)$

Set-Builder Notation:

{x | x > 4}

${x | x > 4}$

Step 4

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$

Set-Builder Notation:

{y | y \in ℝ}

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain:

(4, \infty), {x | x > 4}

$(4, \infty), {x | x > 4}$

Range:

(- \infty, \infty), {y | y \in ℝ}

$(- \infty, \infty), {y | y \in ℝ}$

Step 6

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$