Find the Domain and Range f(x) = square root of (x-1)^2

$f (x) = \sqrt{{(x - 1)}^{2}}$

Step 1

Set the radicand in $\sqrt{{(x - 1)}^{2}}$ greater than or equal to $0$ to find where the expression is defined.

${(x - 1)}^{2} \geq 0$

Step 2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

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

No solution

Step 5

Determine the domain and range.

No solution

Step 6

Find the Domain and Range f(x) = square root of (x-1)^2

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