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Reier to the function f {(6, 9) , (0, 4), (-5, 7), (-2, 2)1. Isr rhat value of _ xIsf ()=7?Tlre value 0f x for which fl) =7 is...

Question

Reier to the function f {(6, 9) , (0, 4), (-5, 7), (-2, 2)1. Isr rhat value of _ xIsf ()=7?Tlre value 0f x for which fl) =7 is

Reier to the function f {(6, 9) , (0, 4), (-5, 7), (-2, 2)1. Isr rhat value of _ xIsf ()=7? Tlre value 0f x for which fl) =7 is



Answers

Find the value of the function for the given value of $x$. $$ f(x)=\left[\frac{x}{4}\right\rfloor, \quad \text { for } x=7 $$

We need to evaluate the following. So we're gonna evaluate the function at -1. So negative one is less than zero. So we're going to use seven x plus three. So we have seven times negative one plus three. This becomes negative seven plus three. So if evaluated at -1 is equal to -4. So F of X F one x zero. We have to use our second equation. We have seven X plus six So equals seven parentheses plus six. We have zero. So this becomes 0-plus six. So the function F evaluated at zero is equal to six. When it's equal to when X is equal to two. We use our second functions so seven X plus six. So that's seven times X plus six. So X is now too. So this becomes 14-plus 6. So the function evaluated at two is equal to 20. So when the function and when F. Is eat when X is equal to four, we use our second function. So we have seven X plus six, so seven times X plus six X is now four, so we get 28 plus six. So the function F evaluated up four is 34.

So we want to evaluate our fallen function and given our ex Follies here, let's find F of two that's equal to 2/7 times two plus four. So we get a 4/7 plus four, which is equal to a four and 4/7. And now we want to find a from zero that's going to be to over seven times their own. I was for it, which is going to get us a four in an F of negative three. We're going to get a 2/7 times. Make it a green plus a four. So we have a minus 12/7. Those four negative 12/7 plus four gives us a two and 2/7.

Now he'll just considered a given function. That is F of X is given to us as minus four x plus seven. And there's another function that is geophysics, which is given to us as X square plus nine X minus two. What do you have to data mine over here? Simply a five of six minus J off six. We have to just find out the value of this given expression. Were you fine? So now to do that, what I'm going to do is I'm going to find out ff six first and then I find out g of six. And then I just subtract with the values so f f six would be founded by by what? Simply I'll be just substituting X s six over here, right? So that would be equal to minus 24 plus seven and minus 24 plus seven gives you more simply minus 17. Similar g Just do the same thing for G of six. G f six will be founded by the sub shooting Xs six in G of six g of x worry. So that would be X square. That is 36 last 19 6 give you 54 minus two. So 36 plus 54 minus two gives you 88. Now F of six minus three of six will be equal to minus 17, minus 88. And that is equal to minus 100. And right, so this is the required answer.

Okay, so it says the function above B is a constant, but it gives you this point right here. So for this we can interpret this as six comments happened because it's typically F of X is equal to some live value. So we know that the ex is whatever's inside the parentheses, and whatever affects is equal to is going to be. Why, so that if we play with the six comma stepping into this original equation weaken basically isolated for the value of B because that at that point, once you've plugged in the points, we only have be very well, so it's just one variable. Someone was going to put that. And so seven is equal to three over two times six must be well, so from here, we know that six times three is eighteen and eighteen, divided by two is just nine. So the seven is equal to nine plus b. Okay, so that from here, if we subtract tonight from both sides, we have seven minus nine is able to be, which is just negative, too center. In order to complete these this equation right here, we're going to say f of X is equal to three over two X minus two so that at that point, if we want to know what f of negative too is, we just have to plug in a negative to every time we see an X. So we're going to say half of negative too is able to three over two times negative to minus two. So from here, three times negative too is negative. Six negative six divided by two is negative. Three, we have the FF. Negative too is equal. Teo once he negative three minus two. Oops, ninety three minutes To which is just gonna become negative five. So a is our answer.


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