Find the Domain and Range y = log base 5 of x-1+3

$y = \log_{5} (x - 1) + 3$

Step 1

Set the argument in $\log_{5} (x - 1)$ greater than $0$ to find where the expression is defined.

$x - 1 > 0$

Step 2

Add $1$ to both sides of the inequality.

$x > 1$

Step 3

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

Interval Notation:

$(1, \infty)$

Set-Builder Notation:

${x | x > 1}$

Step 4

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(1, \infty), {x | x > 1}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6