Statement-1: If `ad-bc ne 0`, then `f(x)=(ax+b)/(cx+d)` cannot attain the value ` {(a)/(c )}` .
Statement-2: The domain of the function `g(x)=(b-dx)/(cx-a)` is `R-{(a)/( c)}`

Options

A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.

Explanation

To solve the given problem, we need to analyze both statements and determine their validity step by step.

### Step 1: Analyze Statement 1
We start with the function:
\[ f(x) = \frac{ax + b}{cx + d} \]

We need to determine if this function can attain the value \( \frac{a}{c} \) given that \( ad - bc \neq 0 \).

#### Step 1.1: Set the function equal to \( \frac{a}{c} \)
We set:
\[ f(x) = \frac{a}{c} \]

This gives us the equation:
\[ \frac{ax + b}{cx + d} = \frac{a}{c} \]

#### Step 1.2: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ c(ax + b) = a(cx + d) \]

#### Step 1.3: Expand both sides
Expanding both sides results in:
\[ acx + bc = acx + ad \]

#### Step 1.4: Simplify the equation
Subtract \( acx \) from both sides:
\[ bc = ad \]

#### Step 1.5: Analyze the condition
Since we know \( ad - bc \neq 0 \), this means \( bc \neq ad \). Thus, the equation \( bc = ad \) cannot hold true, indicating that \( f(x) \) cannot equal \( \frac{a}{c} \).

### Conclusion for Statement 1
Therefore, Statement 1 is **correct**: \( f(x) \) cannot attain the value \( \frac{a}{c} \).

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### Step 2: Analyze Statement 2
Now we need to analyze the function:
\[ g(x) = \frac{b - dx}{cx - a} \]

We need to find the domain of this function.

#### Step 2.1: Identify when the denominator is zero
The function \( g(x) \) is undefined when the denominator is zero:
\[ cx - a = 0 \]

#### Step 2.2: Solve for x
Solving for \( x \) gives:
\[ cx = a \]
\[ x = \frac{a}{c} \]

#### Step 2.3: Determine the domain
The domain of \( g(x) \) includes all real numbers except where the denominator is zero:
\[ \text{Domain of } g(x) = \mathbb{R} - \left\{ \frac{a}{c} \right\} \]

### Conclusion for Statement 2
Therefore, Statement 2 is also **correct**: The domain of \( g(x) \) is \( \mathbb{R} - \left\{ \frac{a}{c} \right\} \).

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### Final Conclusion
Both statements are correct:
- Statement 1: \( f(x) \) cannot attain the value \( \frac{a}{c} \).
- Statement 2: The domain of \( g(x) \) is \( \mathbb{R} - \left\{ \frac{a}{c} \right\} \).

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