The composition of functions involves applying one function to the result of another function. If you have two functions, say $f(x)$ and $g(x)$, the composition of these two functions is written as:

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

This means that you first apply the function $g$ to the input $x$, and then apply the function $f$ to the result of $g(x)$.

Steps for Composing Functions:

1. Start with an input $x$.
2. Apply $g(x)$.
3. Apply $f$ to the result of $g(x)$, which gives $f(g(x))$.

Example:

Let $f(x) = 2x + 1$ and $g(x) = x^2$. The composition $(f \circ g)(x)$ is:

$(f \circ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 1 = 2x^2 + 1$

Would you like more examples or further explanation?

5 Related Questions:

1. How do you compose three functions, say $f(x)$, $g(x)$, and $h(x)$?
2. What is the difference between $f(g(x))$ and $g(f(x))$?
3. Can all functions be composed with each other?
4. How do you find the domain of a composite function?
5. What is the inverse of a composite function?

Tip:

Always check the domain of both functions when composing, as the domain of the composition may be restricted based on the inner function.