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)=-[[-x]], for x=2.5

Accepted Answer

Everyone. In this problem, we are asked to evaluate the value of the following function for X equals 3.5. And the function we're given is F of X is equal to negative the floor of negative X. So these double square brackets indicate the floor function where it's sometimes called the greatest integer function. Okay. You may have heard of either of those terms. Now we have our function And were asked to evaluate it at a particular x value. And in this case that x value is 3.5, What this means is we're gonna take our function f and everywhere there's an X, we're going to replace it by 3.5. And so our function becomes F 3.5 is equal to negative The floor of -3.5. Okay. And this notation on the left f in brackets, 3.5 indicates that we're taking the function f and evaluating it at the x value of 3.5. All right, let's simplify these brackets first. So this is our floor function. If you think about it as a floor function, okay. The floor, if you think of your house or building is underneath you. Okay. It's beneath you. So we want to take the integer that is beneath the value inside our floor function. Okay. So an integer beneath negative 3.5 is negative four. If we want to think of this as the greatest integer function, we can think of it in terms of a number line. So we can draw a number line on the left. We have negative six moving to the right, negative five, negative four, negative three, negative two, negative one. And our value is negative 3.5. So we're going to draw that under a number line and it's gonna be right in the middle of negative three and negative four. And the greatest integer function tells us to take the greatest integer less than the value we're at when we're looking at a number line and we're thinking about a value less than we want to move to the left. The numbers on the left are less than the value we're up. So we're gonna start out our value of negative 3.5. We're gonna move to the left until we hit the next integer. And in this case, that's gonna be negative four and so negative 3.5, the floor or the greatest integer is going to be negative four. And so we end up with negative negative four. Okay. Just be careful. We have this extra negative sign out in front. Um It can be easy to mix up signs when you're dealing with functions like this. So just be careful and always double check and the negative negative four is going to be positive four. And so our function F evaluated that value X equals 3.5 is going to be equal to four. That's going to be answer choice. C Thanks everyone for watching. I hope this video helped you in the next one.

Find the value of the function for the given value of x. See Example 3. ƒ(x)=-[[-x]], for x=2.5

Key Concepts

Function Notation and Evaluation

Floor Function (Greatest Integer Function)

Handling Negative Signs and Nested Functions

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