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

Given:

• $f(x) = x$
• $g(x) = x + 3$

Step 1: Substitute $g(x)$ into $f(x)$

$(f \circ g)(x) = f(g(x)) = f(x + 3)$

Step 2: Replace $x$ in $f(x)$ with $x + 3$

Since $f(x) = x$, we replace $x$ with $x + 3$: $f(x + 3) = x + 3$

Final Answer:

$(f \circ g)(x) = x + 3$

Let me know if you'd like further clarification!

Related Questions:

1. How would you find $g \circ f(x)$ with the same functions?
2. What would happen if $f(x) = 2x$ instead of $x$?
3. Can $(f \circ g)(x)$ ever change if $g(x)$ is a quadratic?
4. What does $(f \circ g)(x)$ represent graphically?
5. How would the solution differ if $f(x) = x^2$?

Tip:

When combining functions, always ensure you substitute correctly and simplify step by step to avoid errors.