Find the Domain and Range f(x)=x+1 if x>1; x-2 if x<=1

$f (x) = {\begin{cases} x + 1 & x > 1 \\ x - 2 & x \leq 1 \end{cases}$

Step 1

Find the domain.

Since the domain of $x + 1$ is all real numbers, the domain of this piece of the function is its restriction, $x > 1$ .

$(1, \infty)$

Since the domain of $x - 2$ is all real numbers, the domain of this piece of the function is its restriction, $x \leq 1$ .

$(- \infty, 1]$

Find the domain by taking the union of all of the intervals where the function is defined.

$(- \infty, \infty)$

Step 2

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

$(- \infty, - 1] \cup (2, \infty)$

Step 3

List the domain and range of the piecewise.

Domain: $(- \infty, \infty)$

Range: $(- \infty, - 1] \cup (2, \infty)$

Step 4