If `f(x)=x-(1)/(x), x ne 0` then `f(x^(2))` equals.

Options

A. f(x)+f(-x)
B. `f(x)f(-x)`
C. `f(x)-f(-x)`
D. none of these

Answer

To solve the problem, we need to find \( f(x^2) \) given that \( f(x) = x - \frac{1}{x} \) for \( x \neq 0 \).

### Step-by-Step Solution:

1. **Identify the function**: We have \( f(x) = x - \frac{1}{x} \).

2. **Substitute \( x^2 \) into the function**: We need to find \( f(x^2) \).
\[ f(x^2) = x^2 - \frac{1}{x^2} \]

3. **Simplify the expression**: The expression \( x^2 - \frac{1}{x^2} \) can be rewritten. We can factor it using the difference of squares.
\[ x^2 - \frac{1}{x^2} = \left( x + \frac{1}{x} \right) \left( x - \frac{1}{x} \right) \]

4. **Recognize that \( x - \frac{1}{x} \) is \( f(x) \)**: From the original function definition, we know that \( f(x) = x - \frac{1}{x} \).
\[ f(x) = x - \frac{1}{x} \]

5. **Substitute back into the factored form**: Therefore, we can express \( f(x^2) \) in terms of \( f(x) \):
\[ f(x^2) = \left( x + \frac{1}{x} \right) f(x) \]

6. **Final expression**: Thus, the final expression for \( f(x^2) \) is:
\[ f(x^2) = \left( x + \frac{1}{x} \right) \left( x - \frac{1}{x} \right) \]

### Conclusion:
The final result for \( f(x^2) \) is:
\[ f(x^2) = x^2 - \frac{1}{x^2} \]