5

5. Express f(2) = (1 + 2)? for 2 € 4(1). Write the formula of when ~...

Question

5. Express f(2) = (1 + 2)? for 2 € 4(1). Write the formula of when ~

5. Express f(2) = (1 + 2)? for 2 € 4(1). Write the formula of when ~



Answers

Evaluate the expression.
$$4 a^{2}+11 \text { when } a=5$$

Moving onto problem. 34 quickness five over a plus minus seven. Or this one equals a squared minus to a class four divided by he squared plus a so again, same pattern pictures where best earn a squared plus eight is this, um can be factored as the to utter denominators. And remember here that our main goal, when trying to solve an equation of this type, is to get rid of those the nominators, Um, because they make your life source. So we want to get rid of them as soon as possible. And one which do this is to multiply everything but every denominator. And that's always possible. That's always an option for you. You couldn't multiply everything by a everything about a plus one. Everything by a squid, A and lots of terms. And you would eventually find solution to this problem. But I think in the previous exercises, what you were trying to make us realize is that you can save a lot of time by factoring. So if this denominator recon factored has, um, as a product of utter the nominators, that's very much worth our time to do it. So we'll do that again here. A squared plus eight. We said it's equaled eight times a plus one, and then you can see this A here, we can find it. Here. This a plus one. We confined here. So it's not like everything but a times a plus one on each side. If we do something on one side, we have to do it on the other side as well. Um, so I'm gonna write it all over again, because I haven't been doing that for the last exercises. So maybe, um, this is gonna help you understand She's still having oh, trouble with this step here for good night. Plus four, um, times eight times. It was one over A. So what I did is I applied this eight times a plus one to every term on both sides of the equation. And then we can cancel ob denominators. There are there is always something of the upper side to cancel them the denominator with And that's because we've been multiplying by term, which, um, is multiplier or which has the denominators as factors. If that makes any sense for you. Um, if if we know that I was just trying to refreeze it here If we know that the term we're miles applying everything with is or has this as a common denominator and this and this, then they won't cancel. Something will cancel on. Did the memories will disappear. Sets. That's how you can choose Ah, which factor use here to best cancer of the denominators. But if if that doesn't work for you, remember that you can always multiply holding by the denominator that's causing you problems. So if this sentiment dominated here was causing the problem with this one, I would just move it by everything that a plus one. Just get rid of those denominators as soon as you can. Um, are do this trick here. Thio Fake factor one that a meter and serve you with time. Let's get going here. Five times, people Swan minus seven. A equals a squared managed to pay us for. So that's, um size, eh? Swung minus seven. A. Equals a squared minus to a plus. For I'm gonna bring, um on a square on the left side or envy every everything on the best time. Basically so you could be right. That is minus X squid. Plus, I am gonna crush them out as I go minus seven A. And then the minus two a day when I bring it to the left side, it becomes plus two A. It's one. Think up. Thus for which becomes makes for. All right, let's open in your dad for that. So minus squared. Plus five a minus seven A plus two A. That's zero. Yeah, that's still the zero. So I didn't write that. And then there's plus one minus four. That's Mr, um indicate something wrong here that could be equal to zero. We just check what happened here. So this a squared is here. Five a. Oh, here's my stake. I didn't do I didn't know about this one by five so awful you could spot that I was just gonna changes as a five and we had this one here, which was a five. Actually, I don't be mean. I'm going to start over from there just to make sure everything is clear, because it would be mean, um, of me to just modify things like that. All right. I'll start over from here, and actually you're Is that because it's all crust gross, Spitter, that takes a little longer and that it's clear. Right? Okay, so I've a plus five here. My seven. A square in minus two. A four. So, no, it's to rest. Let's bring everything to the left. Minus d squared this faith, eh? Crossing them out as I go minus seven. A my plus two A. That's five. And then we got it. Plus four of us is gonna become minus for and we can realize the same thing here is that five plus two minus seven is you. All those terms can't stop you. Sure. And what remains? I don't actually need a new tab because it's gonna be easier than I thought is just minus X squared. Plus one equals zero. Which means that squared equals one A equals plus or minus one. Right. When you have variable squared, you don't know if the variable be positive or negative because both cases will yield same answer. But, um, with those two cases here, plus one minus one, which our God solutions and which ones are not well for this we can look at our top equation. Um, for this denominator, both would be good here. However, if a is equal to minus one. We get zero minus one plus one is zero. And so among those two answers, plus one and minus one, we know that minus one is not possible. Uh, plus one will work, however, because here we have one squared plus one. That's not zero. That's too. So plus one works and plus one is this silly.

You got into pushing and factions given us Do excuse plus X squared. Let's toward it. Minus place No, we have after value is given us fight for here in place off X What will put toe from the left hand relate to Muddy played with took you Plus he multiplied with two square plus four magnetic to minors Play This will be called So this will be ate my blood with 2 16 Listen before it plus eight minus played in court to face for four years ago. Plane Let's play minus eight minus 16. So tell minus this is the miners doing before what that means for a record o minus 10 minus the people So it will do minus 14 divided by four which we can idesk minus seven divided by two So begin to that is equal to minus seven divided by two

Okay, so it's all for falling. So we have a squared A isn't it, too? So we have a negative to to part two plus two times negative two and then or devalue is at six on the plus six quid, so we get four minus a 24 plus in 36. What is that? That's four minutes 24 plus two B six, and that's equal to a 16.

Before I can find the inverse of after the one I first need to find the inverse of death. To do this and going to take the f of x function and replace the f of X with a y equals so that we have why equals two X minus five. Next, I'm going to swap the positions of my variables so that the X takes the place of the why and the why takes the place of the X. This gives me ax equals two. Why minus five. Now I'm going to solve this equation for why or, in other words, isolate the wide variable. To do this I'm going to use inverse operations in verse is just a fancy way of saying opposite. So the opposite or inverse of subtracting five is adding five. And because of properties of the quality, I'm going to add five on both sides of the equation. Negative five plus five cancels out because it equals zero. So we're left with two. Why is equal two x plus five? My wife variable is still not isolated since the two is still there. So once again, using inverse operations or opposite operations, this is two times Why? So the inverse is division, which we show with a fraction bar. And once again because of properties of equality. If I divide by two on one side of the equation, I have to divide by two On the other. Notice I divide the entire expression X plus five by the two on the right side, two divided by two cancels out, leaving us with just why and on the left side we have X plus five divided by two. Now that I have isolated my Y variable, I can reinsert the inverse notation So the inverse of FX is equal. Two. X plus five divided by two. Now I am able to actually find the inverse of f of one. To do this, I'm going to substitute a one in for the X variable. In our function, this will look like one plus five. Divided by two. One plus five is six. So we're doing six. Divided by two and six. Divided by two is three. So the inverse of


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