To find $(f - g)(x)$, we need to subtract the function $g(x)$ from $f(x)$.

Given:

• $f(x) = \sqrt{1 - x^2}$
• $g(x) = \frac{1}{x + 1}$

Now, $(f - g)(x)$ is calculated as follows:

$(f - g)(x) = f(x) - g(x)$

Substitute the given functions:

$(f - g)(x) = \sqrt{1 - x^2} - \frac{1}{x + 1}$

So, the expression for $(f - g)(x)$ is:

$(f - g)(x) = \sqrt{1 - x^2} - \frac{1}{x + 1}$

This is the final answer.

Would you like a more detailed explanation or have any further questions?

Here are some related questions to explore:

1. How do you differentiate the function $(f - g)(x)$?
2. What are the domains of $f(x)$ and $g(x)$?
3. What happens if we add the functions $f(x)$ and $g(x)$ instead of subtracting them?
4. How would you evaluate $(f - g)(x)$ for a specific value of $x$?
5. Can you apply the concept of limits to this function as $x \to 0$?

Tip: Always check the domain of each function to ensure that the operations you perform (like addition, subtraction, or division) are valid across the entire domain.