Calculus Examples

$f (x) = x \ln (x)$

Step 1

Set the argument in $\ln (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

Step 2

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

Interval Notation:

$(0, \infty)$

Set-Builder Notation:

${x | x > 0}$

Step 3

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[- \frac{1}{e}, \infty)$

Set-Builder Notation:

${y | y \geq - \frac{1}{e}}$

Step 4

Determine the domain and range.

Domain: $(0, \infty), {x | x > 0}$

Range: $[- \frac{1}{e}, \infty), {y | y \geq - \frac{1}{e}}$

Step 5