Statement -1 If `f(x)` and g(x) both are one one and `f(g(x))` exists, then `f(g(x))` is also one one.
Statement -2 If `f(x_(1))=f(x_(2))hArrx_(1)=x_(2)`, then `f(x)` is one-one.

Options

A. Statement -1 is true, Statement -2 is true and Statement -2 is correct explanation for Statement -1
B. Statement -1 is true, Statement -2 is true and Statement -2 is not correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false Statement -2 is true

Explanation

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

### Step-by-Step Solution:

**Step 1: Analyze Statement 1**
- Statement 1 claims that if both functions \( f(x) \) and \( g(x) \) are one-to-one (injective) and \( f(g(x)) \) exists, then \( f(g(x)) \) is also one-to-one.
- A function is one-to-one if it maps distinct inputs to distinct outputs.

**Step 2: Understand the implications of \( g(x) \) being one-to-one**
- Since \( g(x) \) is one-to-one, for any two distinct inputs \( x_1 \) and \( x_2 \), if \( x_1 \neq x_2 \), then \( g(x_1) \neq g(x_2) \). This means that \( g \) does not map different inputs to the same output.

**Step 3: Understand the implications of \( f(x) \) being one-to-one**
- Since \( f(x) \) is also one-to-one, if \( f(g(x_1)) = f(g(x_2)) \), then it must follow that \( g(x_1) = g(x_2) \) (because \( f \) does not map different inputs to the same output).

**Step 4: Combine the implications**
- From the above, since \( g(x_1) \neq g(x_2) \) for \( x_1 \neq x_2 \), it follows that \( f(g(x_1)) \neq f(g(x_2)) \).
- Therefore, \( f(g(x)) \) is one-to-one.

**Conclusion for Statement 1:**
- Statement 1 is true.

**Step 5: Analyze Statement 2**
- Statement 2 states that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \), which is the definition of a one-to-one function.
- This means that if two outputs of the function \( f \) are equal, their corresponding inputs must also be equal.

**Conclusion for Statement 2:**
- Statement 2 is also true.

### Final Conclusion:
- Both Statement 1 and Statement 2 are true. Statement 2 serves as a correct explanation for Statement 1.