Find the value of the function for the given value of x. ƒ(x)=...

Question

Find the value of the function for the given value of x. ƒ(x)=[[x]], for x=-√2

Accepted Answer

Hey, everyone in this problem, we are asked to evaluate the value of the following function for X is equal to negative two root three. And the function we're given is F of X is equal to the floor of X. Okay. So these square double square brackets that you see in this function that represents the floor function or sometimes it's called the greatest integer function. Alright, so we have our function F of X is equal to the floor for the greatest integer of X and were asked to evaluate it at X equals negative two root three. And what that means is we're gonna substitute X equals negative two root three into this function. Okay. So everywhere we see an X, we replace it with negative two root three. So we have F at negative two root three Is equal to the floor of -2 or three. Now these square brackets act a little bit like normal brackets. So just like we have normal brackets, we want to evaluate what's inside the brackets first. Okay. So let's do that. So we have the floor and negative two or three is going to be negative 3.46 approximately. Now this greatest integer function or the floor function takes the greatest integer less than the entered your world. Okay. So if you imagine drawing a number line, we have negative one, negative two, negative three, negative four, negative five And our value is negative 3.46. So it's somewhere right around here between -3 and -4. And you want to take the greatest integer lesson. Okay. So when you're looking at a number line numbers that are less than the number we're at are to the left. Okay. So we go to the left. The first integer we hit is negative for okay. And so the greatest integer less than negative 3.46 or the floor of negative 3.46 is going to be negative four. And that is our function evaluated that X value. So if we look at our answer choices, we see that that corresponds with answer choice C F of X equals the floor of X evaluated at X equals negative two root three is equal to negative four. That's it for this one. Thanks everyone for watching. See you in the next video.

Find the value of the function for the given value of x. ƒ(x)=[[x]], for x=-√2

Key Concepts

Floor Function (Greatest Integer Function)

Evaluating Functions at Specific Values

Properties of Square Roots and Negative Numbers

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