To find $(f \circ g)(x)$, we compute $f(g(x))$, which means substituting $g(x)$ into $f(x)$.

Given:

1. $f(x) = x + 2$
2. $g(x) = 2x^2 + 3x + 6$

Steps:

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

2. Using $f(x) = x + 2$, replace $x$ in $f(x)$ with $g(x)$: $f(g(x)) = (2x^2 + 3x + 6) + 2$

3. Simplify: $f(g(x)) = 2x^2 + 3x + 6 + 2$ $f(g(x)) = 2x^2 + 3x + 8$

Final Answer:

$(f \circ g)(x) = 2x^2 + 3x + 8$

Would you like a breakdown of the substitution process or help with a similar problem?

Relative Questions:

1. How do you compute $(g \circ f)(x)$?
2. What are the conditions for $f \circ g = g \circ f$?
3. How does the domain of $g(x)$ affect $f(g(x))$?
4. Can $(f \circ g)(x)$ ever equal $g(x)$?
5. How do you find the inverse of a composite function like $(f \circ g)(x)$?

Tip: Always double-check your substitution and simplification steps to avoid errors in composite functions.