1.5 Function Composition

3 practice questionsNot yet reviewed

Notes

Composition plugs one function into another: $(f \circ g)(x) = f(g(x))$.

Work from the inside out: find $g(x)$ first, then put that result into $f$.
Order matters: $f(g(x))$ is usually not equal to $g(f(x))$.
Example: $f(x) = 2x + 1$, $g(x) = x^2$. Then $f(g(3)) = f(9) = 19$, but $g(f(3)) = g(7) = 49$.
As a formula: $f(g(x)) = 2x^2 + 1$.

Let $f(x) = 2x + 1$ and $g(x) = x^2$. Find $f(g(3))$.

With the same functions, find $(g \circ f)(x)$.

Let $h(x) = x - 3$ and $k(x) = 5x$. Find $k(h(x))$.