Find the value of the function for the given value of x. See Exam...

Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=x-(-π)

Accepted Answer

Hey, everyone. Welcome back. In this problem, we are asked to evaluate the value of the following function for X equals negative two pot. The function we're given is FF X is equal to the floor of X. OK. So these double square brackets represent the floor function and sometimes it's called the greatest infantry function. So either one of those terms. And so when we have a function that's a fix And were asked to evaluate it at a particular x value. In this case, X is equal to two pi what we do is we take that X value and we substitute it into our function everywhere where we have an X okay. And so we end up with our function evaluated at negative two P Is equal to the floor. They are the greatest integer of -2 pi just like when we have regular brackets, we want to evaluate what's inside the brackets first. Okay. So before we evaluate the floor of this number inside, we have to figure out what that number is. And so we have negative two pi and so this is going to be approximately The floor of -6.28. Okay. Now we're taking the floor function. Um, we don't need a ton of decimal places because the floor function is going to kind of round or truncate this off to the nearest integer anyways. Okay. So we're okay with two decimal places here just to kind of figure out where that value falls. Okay. Now, the floor function or the greatest integer function is going to take the greatest integer less than the one we have. Okay. So if we imagine a number line and we have our values negative six, negative seven, negative eight and then negative five, negative four. Okay. Alright. So our value is negative 6.28. It's somewhere around here Okay. Between -6 and -7. Now the greatest integer or floor function is going to take the greatest integer lesson when we're looking at our number line and we're talking about lesson that's going to be to the left. Okay. So if we go to the left until we hit the next integer, that's going to be negative seven. So the greatest imager less than negative 6.28 is -7. And so our function evaluated at negative two pi is going to be equal to negative seven. Okay. If we look at our answer traces, that's going to correspond with answer choice. A thanks everyone for watching. I hope this video helped you in the next one.

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Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=x-(-π)