In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find...

Question

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g(-1) and f(g(-1)).

Accepted Answer

Welcome back. I'm so glad you're here. We have two equations here. F of X and G of X. I'll rewrite those. We have F of X equals X cubed minus two, X squared plus X plus one and G of X equals the square root of one minus X squared. We are to find out first G of negative one and then we're to find out F of G of negative one. So let's go ahead and work on G of negative one which means instead of G of X, it's G of negative one meaning anywhere there was an X. We're going to plug in a negative one so now it's one minus negative one squared. Okay, let's do the math. We've now got the square root of a working inside the radical, we start off with negative one squared and negative one squared is just one. So we've now got 1 -1 And now we keep working inside the radical 1 -1. Well I don't need that big of a radical anymore because 1 -1 is zero. So we've got the square root of zero and the square root of zero is just zero. So G of negative one equals zero. The next thing we're asked to find is F of G of negative one, meaning that instead of X we're supposed to plug in I'll use a different color instead of X. We're supposed supposed to plug in G of negative one which as we've proved over here is zero. So this is the same thing as F of zero. Well plugging in zero for X cubed is going to be zero cubed minus two times. Well that will be zero squared plus instead of X. That's zero plus one. Alright, well that's simplifying isn't going to take too long. Zero cubed minus two times zero squared plus zero. All of that is just zero. So we're left with F of G of negative one equals just one. We look at our answer choices and that matches with answer choice. B. Well done, we'll catch you on the next one.

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