To find $(f \circ f)(x)$, we need to calculate the composition of the function $f(x)$ with itself.

Given:

• $f(x) = x + 2$

Now, $(f \circ f)(x)$ means $f(f(x))$. We substitute $f(x)$ into itself:

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

To find $f(x + 2)$, substitute $x + 2$ into the function $f(x)$:

$f(x + 2) = (x + 2) + 2 = x + 4$

Thus, $(f \circ f)(x) = x + 4$.

Let me know if you would like any further clarifications! Here are some related questions for further practice:

1. What is $(f \circ h)(x)$ if $h(x) = x^2 - 3$?
2. How would you calculate $(h \circ f)(x)$?
3. What is the result of $(f \circ f \circ f)(x)$?
4. How does the behavior of the function $f(x) = x + 2$ change as you repeatedly compose it with itself?
5. If $f(x) = 2x$, what would $(f \circ f)(x)$ be?

Tip: Composition of functions can be thought of as substituting one function's output into another's input.