To find $(f \circ g)(x)$, which is the composition of $f(x)$ and $g(x)$, we substitute $g(x)$ into $f(x)$. The composition $(f \circ g)(x)$ means $f(g(x))$.

Given:

• $f(x) = x^2 + 6$
• $g(x) = x^2$

Step-by-step:

1. Find $g(x)$:
   $g(x) = x^2$

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

3. Substitute $x^2$ into $f(x)$:
   $f(x^2) = (x^2)^2 + 6 = x^4 + 6$

So, $(f \circ g)(x) = x^4 + 6$.

Would you like a more detailed explanation or further clarification?

Here are some related questions you might find useful:

1. What is the result of $(g \circ f)(x)$ with the same functions?
2. What happens when you change $f(x)$ or $g(x)$ in the composition?
3. How does the degree of the polynomial change in compositions of functions?
4. How can we verify if $f \circ g$ is one-to-one or onto?
5. What are the graphical interpretations of composed functions?

Tip: When composing functions, always start with the innermost function and substitute it into the outer function!