5

7) Find a function f(x) with the following property: f(x)f(2) = 0...

Question

7) Find a function f(x) with the following property: f(x)f(2) = 0

7) Find a function f(x) with the following property: f(x) f(2) = 0



Answers

Find the zero of each function.
$$
f(x)=7-x
$$

Or the limit definition I'm the derivative Is equal to the limit as H approaches zero of F. Of X passage -1 A bex all over. H. 12. For examining alphabet X equal seven. Uh Well, there's no extra plug into this problem. So if you also examine F. Of X plus each. Well if you replace X with X plus H, there's no extra plate. So it's still just seven. So when you look at this problem Uh the derivative of this function seven would be equal to assert your degree to limit As a church approaches zero of replaced. This was seven because that's what's equal to Replacing this with seven because that's what that is equal to all over each. And so when you look at that, we're looking at um seven minus seven which equals zero. So its limit as H approaches zero A zero over H. Now technically speaking um we can't do a direct substitution. Um And at this point I'm just going to let you believe me that zero divided by this value is going to be equal to zero. Um You could use for future people. There's something called Loki tells rule that would uh make this applicable. Um But for our purposes let's just examine that zero divided by some value because we're doing the limit. So H is approaching that value. So 0 to 5.1 is still 00- 5.01. Um And it's the same thing with negative value. So this is true. zero is your answer.

So let's find the function of zero. Here we go. Uh, let's put zero into X here now. Zeer negative. Four times zero is zero and zero plus seven is seven. So the function R of zero or F zero equals seven.

So here's our function. We have f of X equals seven x squared. I'm gonna try to find the derivative of this. We're gonna use something called the power rule. So the power roll comes in the form generally accident. So here we have X greater and would be too. So if we use the drone of this of this private situation we get and times X to the N minds work. So you bring this power down and then reduce the power by one. So back to here with F Problem X, which is the first derivative, take the two down and then reduce it by one. So just be except for one. And we can further simplify this toe 14 x and that's your answer.

Okay, so we're given this function f of X and were asked to evaluate it for 20 and negative one. So let's find f of two by substituting to into the function for X. So we get to plus eight over two times two minus one. And now we're just using order of operations to simplify. The numerator simplifies to be 10 and the denominator simplifies to be three. So the answer to that one is 13th moving on to f of zero. Well, substitute zero into the function for X. So we get zero plus eight over two times zero minus one, and that gives us eight over negative one. And we could just call that negative eight and then finally up of negative one will substitute negative one into the function for X. And then when we simplify the numerator, we get seven on dhe. When we simplify the denominator, we get negative three and we could leave it at that or we could just call it negative 7/3


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