Composite Functions Don’t Have to Be Complicated 🔥 #education #studytips #testprep #math

Added: 2026-05-17

[00:00:00]Let's take a look at the fastest way to get through this ACT math question that deals with composite functions. Now in this case we're going to start from the most inside part, which is our G of X, and that's going to become our input into our f of x equation. So we're going to take f of 3x - 1, and that means every single place we see an x in our f of x equation, we're going to replace that with 3x - 1. So we're going to have 3x - 1 quantity squared + 2 * 3x - 1 - 5. So we have to make sure that we're going to foil or distribute everything that we're putting in place here. So this is going to give us 9x squared - 6x + 1 + 6x - 2 - 5. So in this case I want to quickly compare to my answer choices, and I can see that I only have one nine or one x squared polynomial in this, so I'm going to eliminate answer choice A.

[00:01:07]When we take a look at what else we have here, I want to see what I can do in terms of getting to my last value, because that's also going to be easy as well. We have + 1 - 2 and - 5. That's going to give me a total of - 6 there.

[00:01:23]So I'm going to eliminate answer choice C as a result of that. And now we can quickly see we save those middle terms for last because they tend to be a little bit stickier or more time consuming. These are indeed going to cancel themselves out, and we do not have a middle term, so I'm choosing answer choice B.