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

Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[0.5x]], for x=7

Accepted Answer

Hey, everyone in this problem, we are asked to evaluate the value of the following function for X equals nine. And the function we're given is F of X is equal to the floor of 0.8 X. Okay. So these double square brackets indicate the floor function or it's also called the greatest integer function. You may have heard either of those terms in your course. Now we have a function F And were asked to evaluate it at a particular x value. And in this case that X value is X is equal to nine. What this means is we want to take our function and everywhere there's an X term, we're going to replace it with the value nine. So we get f at nine. Okay. This notation indicates we take the function F and evaluated the X value X equals nine K F with nine and brackets beside it. And this is equal to 0. times nine. Can we close off those brackets? Now, before we can evaluate this floor function, we need to simplify what's inside the brackets. If we do that 0.8 times nine, gives us a value of 7.2. And now we can evaluate this floor function. So we think of it as a floor function, okay the floor, You know, in your home and a building is underneath you beneath you. So we want the integer that's beneath 7.2 which is going to be set. We can also think of this as the greatest integer on a number line. So if we have three four, and 9 on the number line K from left to right, And we put our .7.2. So it's gonna be between seven and eight, a little closer to seven. Now, the greatest integer function wants you to take the greatest integer less than The value you have. Okay. So if we're talking about a number line and we want to value that's less, then that's going to be to the left on the number line, the numbers to the right or greater than the numbers on the left are less than. So we're gonna move from our value 7.2 to the left on our number line until we hit an integer. And in this case that first introduced we hit is going to be seven. Okay. So either way you think about this function, whether you think about it as a floor or greatest integer It is going to give us a value of seven. And so that is our function evaluated, our function evaluated at X equals nine. Is going to be equal to seven and that corresponds with answer choice A 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. See Example 3. ƒ(x)=[[0.5x]], for x=7

Key Concepts

Function Notation

Floor Function

Evaluating Functions at a Given Input

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