in-3-10-find-each-of-the-function-values-when-mathrmfx4-x-mathrmfleftmathrmf-1-6right

Question

In $3-10,$ find each of the function values when $\mathrm{f}(x)=4 x$
$$
\mathrm{f}\left(\mathrm{f}^{-1}(-6)\right)
$$

Shira Strong · Accepted Answer

Hi, everybody. The deception 4.8. Number eight on it. It says that f of X is equal to four X and we have to find f of F in verse of negative six. So there are a few ways to go about this problem. One way to do it is let&#x27;s first find the inverse. How do you find the inverse of the function? Well, this function is why equals four X. And to find the inverse, we have to switch the X and Y so X is equal to four. Why, Uh, okay, and now we want to solve for the new Why. So we divide both sides by four, and we get why is equal to X over four. So that is our inverse function. F in verse is X over four. So if we plug in a negative six f inverse of negative six would be negative. Six over four or it reduces to negative three halves. Now we want to find f of negative 3/2 how we find f of negative three halves. We plug it into the X right here. So it&#x27;s four x. What is X negative? Three over two on When we evaluate this, we get four times negative. Three over two is negative. 12 over, too is negative. Six. And that&#x27;s our answer. Well, what do you notice? Look at the question and look at the answer. Well, ah, function and its inverse right. What&#x27;s gonna happen when you compose them? You get X, you get what you plugged in. So because this was the question, this is going to be the answer. There&#x27;s no issue with restrictions. This is a linear function. The answer is negative. Six. So you could have done it the short way or the longer way.

Aryan Malesha · Answer

Okay, so for this problem, we know that after Vex equals four ax and basically we&#x27;re trying to find us in verse of of six. So as we can see here, we know that we have a inverse here. So the first step is basically just gonna be to figure out what is the inverse of the function aftereffects. Once we have that equation down, we can go about solving this. So that&#x27;s f of X. And then if we try to find the inverse weaken start by rewriting this is why equals four X. Now let&#x27;s switch the X and y X equals for what to solve for the inverse divide both sides by four four and then we end up with y equals X over for So basically, we know that the inverse that&#x27;s the inverse of X is acts over. For now. We can kind of put these numbers in and solve the equation. So first we want to start with this inside piece. So let&#x27;s see what is f of six. So you know that from six equals four times six because we just played about six into that expression, and we end up with 24 For that. Four times six is 24. Now. Now that we know f of six, we want to go back to our original things. So we have. What we have left is F inverse of 24. Now let&#x27;s tryto figure this out. And if we plug this into the equation for the for F in verse that we got, we can do plug that in as 24/4, which gives us the result of six. So basically what that means is, given this information, we know that f in verse that&#x27;s a six equals six. And that does check out because the f inverse and the regular function f basically cancel out, leaving us with six.

Aryan Malesha · Answer

Okay, so here we have a function that is after Lex equals four X. And what we&#x27;re trying to find is S of I of three, where I is the inverse of FX. Basically, just looking at this, we can kind of try to derive the answer. So we&#x27;re plugging the inverse back into the original function, which basically means that we&#x27;re gonna end up with whatever is inside there. So three. But you know what? Let&#x27;s come to try it out and see if that works. So it&#x27;s find the inverse for So let&#x27;s kind of write this as for equals or why equals four X and then we&#x27;re gonna switch the X and the y so we can start going about solving for the inverse Isolate the wine out to get the inverse, so divide both sides by four. And here we have the inverse, which is why equals Oops, sorry. That should be Why equals X over for that? There is are inverse function. No, we can plug use that function and plug it in here. So I have three equals and then we can sub in the three. So we&#x27;re gonna get 3/4 now. We want to look at us of 3/4 because whatever we get from here is going to go into I sub sub in for this so f of 3/4. Let&#x27;s go back to this original equation that&#x27;s gonna give us for Times X, which in this case is going to be three over for it and the&#x27;s force cancel out. So we&#x27;re left with just three as our final answer. That is correct.

Shira Strong · Answer

Hi, everybody. We&#x27;re going to do Section 4.8, Number six where they tell you that F of X is equal to four X. And then the question they want to know is, what is I of f of two? So this is a composition of function. So whenever we compose functions, we always work from the inside out. So let&#x27;s start on the inside and find f of two. Well, they again. They told us that F of X is for X, so f of two says replace the X value is too, so it would be four times to which is eight. So we just found out that effort to is eight. And what will I of eight be? That&#x27;s the question. Well, I is. The identity function on the identity function is when y is equal to x. Your influence the same as your output. So if your input is eight, your output would also be eight. So the answer is eight

Aryan Malesha · Answer

Okay, So for this problem, we know that function f of X equals for X and are trying to find the inverse value. So basically, we&#x27;re trying to find when what happens with the inverse when you plug in three. So let&#x27;s kind of start by just figuring out what is the inverse of dysfunction. So it&#x27;s kind of right, and that&#x27;s why equals four X just to make a little easier to work with. We switched around the X and the Y and let&#x27;s isolate why. So we divide these fried by four and we&#x27;re left with y equals X over for that right there is the inverse. So take that here and then here we can kind of plug in this. So we plug in the three for X and we end up with 3/4 is our final answer. Check that off.

Shira Strong · Answer

Hi, everybody. We&#x27;re going to do Section 4.8 Problem number four, where they tell you that F of X is equal to four acts and then they ask you to find eye of five. So first of all, just to explain, there&#x27;s no f in the question we were asked. So this piece of information that&#x27;s on top has nothing to do with the problem. It&#x27;s actually a relevant, so I&#x27;m gonna cross it off. Only reason it&#x27;s there. It&#x27;s for the whole section. So what is I of five? I is the identity function. Identity function is when y is equal to X, that they&#x27;re the same value. So this is your F of X and X is five. Well, if why&#x27;s the same thing? What&#x27;s the answer? Gonna bay answers. Just going to be five. That&#x27;s what the identity function is. The input is gonna be the same as the output

Problem

In $3-10,$ find each of the function values when …

Problem 8 Medium Difficulty

In $3-10,$ find each of the function values when $\mathrm{f}(x)=4 x$
$$
\mathrm{f}\left(\mathrm{f}^{-1}(-6)\right)
$$

Answer

$-6$

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