I'm assuming since there is no question, that you want an explanation for composite functions.
Today, I want to introduce you to a very new way of looking at functions. Think of a function as a machine. I'll call this machine f. When you plug something into this machine, it is an x-value. The machine changes the x-value into a new value which is called a y-value. This is how a function works.
With composite functions though, things get a little bit tricky. To make f(g(x)), you need to plug in x into the g machine, and it will give you an output. (y-value) The next thing you do is take that y-value and plug it into the g machine. The g machine then gives you a new value. This value is f(g(x)).
Let's do an example together... f(x)=3x and g(x)=x²+4 if we want f(g(x)), first plug in x to the g machine. when plugging in x to the g machine, we get x²+4 as given in the question. Now we must plug in g(x) into the f machine. Since g(x) is x²+4, we just replace x with x²+4. We get 3(x²+4) This means that f(g(x))=3(x²+4)
NOTE: If you are seeking help with an actual question, please message me in the comments and I will assist you shortly!
