Find domain of `f(x)=log_(10)(1+x^(3))`.

Answer

To find the domain of the function \( f(x) = \log_{10}(1 + x^3) \), we need to determine the values of \( x \) for which the expression inside the logarithm is positive. The logarithm is defined only for positive arguments.

### Step-by-Step Solution:

1. **Set the argument of the logarithm greater than zero**:
\[ 1 + x^3 > 0 \]

2. **Rearrange the inequality**:
\[ x^3 > -1 \]

3. **Take the cube root of both sides**:
\[ x > \sqrt[3]{-1} \]
Since \( \sqrt[3]{-1} = -1 \), we have:
\[ x > -1 \]

4. **Write the domain in interval notation**:
The solution \( x > -1 \) means that \( x \) can take any value greater than \(-1\). Therefore, the domain of the function is:
\[ (-1, \infty) \]

### Final Answer:
The domain of \( f(x) = \log_{10}(1 + x^3) \) is \( (-1, \infty) \).