If `f(x)=x^(3)-(1)/(x^(3))` , then find the value of `f(x)+f(-x)` .

Explanation

To solve the problem, we need to find the value of \( f(x) + f(-x) \) given that \( f(x) = x^3 - \frac{1}{x^3} \).

### Step-by-Step Solution:

1. **Write down the function:**
\[ f(x) = x^3 - \frac{1}{x^3} \]

2. **Find \( f(-x) \):**
To find \( f(-x) \), we replace \( x \) with \( -x \) in the function:
\[ f(-x) = (-x)^3 - \frac{1}{(-x)^3} \]
Simplifying this gives:
\[ f(-x) = -x^3 - \left(-\frac{1}{x^3}\right) = -x^3 + \frac{1}{x^3} \]

3. **Add \( f(x) \) and \( f(-x) \):**
Now we add \( f(x) \) and \( f(-x) \):
\[ f(x) + f(-x) = \left( x^3 - \frac{1}{x^3} \right) + \left( -x^3 + \frac{1}{x^3} \right) \]
Combining the terms:
\[ f(x) + f(-x) = x^3 - \frac{1}{x^3} - x^3 + \frac{1}{x^3} \]

4. **Simplify the expression:**
Notice that \( x^3 \) cancels with \( -x^3 \) and \( -\frac{1}{x^3} \) cancels with \( \frac{1}{x^3} \):
\[ f(x) + f(-x) = 0 \]

Thus, the final result is:
\[ f(x) + f(-x) = 0 \]