Describes fog and gof, where :
`f(x)=sqrt(1-x^(2)),g(x)=logx`

Answer

To describe \( f \circ g \) and \( g \circ f \) for the functions \( f(x) = \sqrt{1 - x^2} \) and \( g(x) = \log x \), we will follow these steps:

### Step 1: Calculate \( f(g(x)) \)

1. Start with the function \( g(x) \):
\[ g(x) = \log x \]
2. Now substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f(\log x) \]
3. Since \( f(x) = \sqrt{1 - x^2} \), we replace \( x \) with \( \log x \):
\[ f(g(x)) = \sqrt{1 - (\log x)^2} \]

### Step 2: Calculate \( g(f(x)) \)

1. Start with the function \( f(x) \):
\[ f(x) = \sqrt{1 - x^2} \]
2. Now substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(\sqrt{1 - x^2}) \]
3. Since \( g(x) = \log x \), we replace \( x \) with \( \sqrt{1 - x^2} \):
\[ g(f(x)) = \log(\sqrt{1 - x^2}) \]
4. This can be simplified using logarithmic properties:
\[ g(f(x)) = \frac{1}{2} \log(1 - x^2) \]

### Final Answers
- \( f(g(x)) = \sqrt{1 - (\log x)^2} \)
- \( g(f(x)) = \frac{1}{2} \log(1 - x^2) \)