The domain of definition of the function `y=3e^(sqrt(x^(2)-1))log(x-1)` is

Options

A. `(1,oo)`
B. `[1,oo)`
C. `R-{1}`
D. `(-oo,-1)uu(1,oo)`

Answer

To determine the domain of the function \( y = 3e^{\sqrt{x^2 - 1}} \log(x - 1) \), we need to analyze the components of the function to find the values of \( x \) for which the function is defined.

### Step 1: Analyze the square root term
The expression \( \sqrt{x^2 - 1} \) is defined when the argument is non-negative:
\[ x^2 - 1 \geq 0 \]
This simplifies to:
\[ x^2 \geq 1 \]
Taking the square root of both sides gives:
\[ |x| \geq 1 \]
This means:
\[ x \leq -1 \quad \text{or} \quad x \geq 1 \]

### Step 2: Analyze the logarithmic term
The expression \( \log(x - 1) \) is defined when its argument is positive:
\[ x - 1 > 0 \]
This simplifies to:
\[ x > 1 \]

### Step 3: Combine the conditions
From Step 1, we have two ranges: \( x \leq -1 \) or \( x \geq 1 \). From Step 2, we have \( x > 1 \).

The only overlapping condition that satisfies both steps is:
\[ x > 1 \]

### Conclusion
Therefore, the domain of the function \( y = 3e^{\sqrt{x^2 - 1}} \log(x - 1) \) is:
\[ \text{Domain: } (1, \infty) \]