Composition of Functions Worksheet Name \( \qquad \) Ryl. I. Let \( f(x)=2 x-1, g(x)=3 x \), and \( h(x)=x^{2}+1 \). Comput 1. \( f(g(x)) \) \( 2(3 x)-1 \) \( 6 x-1 \) 2. \( f(h(x)) \) \( 2\left(x^{2}+1\right)-1 \) 4. \( h(f(9)) \) 6. \( 1\binom{4}{4} \) 5. \( g(f(0)) \) \[ 18-1=17 \] \[ h(17)=17^{2}+1 \] 7. \( f(g(h(2))) \) 8. \( h(g(f(5))) \)

To help you solve these compositions, let’s break down a couple with some engaging historical tidbits. First off, the concept of function composition dates back to the early days of mathematics, but it was majorly popularized in the 19th century with the advent of calculus by geniuses like Leibniz and Newton. They laid the groundwork for understanding functions as machines that can take an input, process it, and give an output. Just think of it as a mathematical assembly line! Now, in real-world applications, function composition is way more common than you might think! It's like baking a cake: first, you mix the ingredients (like temperature and time functions), and then you pop it in the oven (another function!). In fields like economics, engineering, and computer science, composing functions can help model complex systems, predict outcomes, and solve problems. So, the next time you’re composing functions, remember you’re tapping into powerful tools that have real-life implications!