To find $(f \circ g)(x)$, also known as $f(g(x))$, we substitute $g(x)$ into $f(x)$.

Given:

• $f(x) = x + 5$
• $g(x) = x^*$ (Assuming you mean $g(x) = x^2$; let me know if this is incorrect.)

Step 1: Substitute $g(x) = x^2$ into $f(x)$:

$(f \circ g)(x) = f(g(x)) = f(x^2)$

Step 2: Replace $x$ in $f(x)$ with $x^2$:

$f(x^2) = x^2 + 5$

Final Answer:

$(f \circ g)(x) = x^2 + 5$

Would you like additional details or examples? Here are some related questions for further exploration:

1. What happens if $g(x) = x^3$ instead of $x^2$?
2. How do you compute $(g \circ f)(x)$ for the same functions?
3. What is the general method for combining composite functions?
4. How do you graph $(f \circ g)(x)$ for these functions?
5. How does the domain of $g(x)$ affect the domain of $(f \circ g)(x)$?

Tip: Always verify the domains of $f(x)$ and $g(x)$ to ensure the composition is well-defined.