What is the domain of the function f(x)= 1/(x-1).a.R/ {3}b.Rc.R/ {1}d.R/{-3}Clear my choice

Step 1: Break Down the Problem

To find the domain of the function $f(x) = \frac{1}{x - 1}$, we need to identify the values of $x$ for which the function is defined. Specifically, we need to check where the denominator equals zero, as division by zero is undefined.

Step 2: Relevant Concepts

The function $f(x)$ is defined for all real numbers except where the denominator is zero.

Step 3: Analysis and Detail

Set the denominator equal to zero to find the restriction on $x$: $x - 1 = 0$

Solving for $x$: $x = 1$

Thus, the function $f(x) = \frac{1}{x - 1}$ is undefined at $x = 1$. Therefore, the domain excludes this value.

Step 4: Verify and Summarize

Since the function is defined for all real numbers except for $x = 1$, the domain is $\mathbb{R} \setminus \{ 1 \}$.

Final Answer

The domain of the function $f(x) = \frac{1}{x - 1}$ is $\mathbb{R} \setminus \{ 1 \}$, which corresponds to option c. $\mathbb{R} \setminus \{1\}$.