Questions: What is the domain of the function f(x) = sqrt(x-1)^2 ? (Enter r for all Real numbers.)

What is the domain of the function f(x) = sqrt(x-1)^2 ? (Enter r for all Real numbers.)
Transcript text: What is the domain of the function $f(x)$ $=\sqrt{(x-1)}^{2}$ ? (Enter $r$ for all Real numbers.)
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Solution

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Solution Steps

Step 1: Identify the Parity of n and Determine the Approach

The given function is $f(x) = \sqrt{(x - 1)^2}$ with $n = 2$ and $h = 1$.

Step 2: Apply the General Solution Approach Based on the Parity of n

Since $n = 2$, the domain of $f(x) = (\sqrt{x - 1})^2$ is determined by setting the expression inside the square root to be greater than or equal to zero, i.e., $x - 1 \geq 0$. This gives $x \geq 1$. Thus, the domain is $[1, \infty)$.

Final Answer: The domain of the function is $[1, \infty)$.

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