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)=2-[[-x]], for x=3.7

Accepted Answer

Hey, everyone in this problem, we're asked to evaluate the value of the following function for X is equal to 5.8. And the function we're given is F of X is equal to four minus the floor of negative X. OK. And so these double square brackets indicate the floor function or you may have also heard it called the greatest integer function. OK. Those two mean the same thing. And so we have our function F and when we're asked to evaluate a function at a particular X value in this case, that X is equal to 5.8. And what that means is we're gonna replace all the XS in our function with this value of 5.8. So we have fa evaluated at 5.8. OK. This notation F in brackets, 5.8 means we're taking the function F and evaluating it the X value 5.8. And this is gonna be equal to four minus any square brackets indicating the floor function negative 5.8. And then we close out those brackets. All right. So let's deal with these brackets first. OK. So we have the floor of negative 5.8. But we think of this as the floor function, OK? When you think about a floor, the floor is beneath you. OK? So we wanna take the greatest integer that is beneath our number negative 5.8 which is gonna be negative six. OK? We can also think about this if you want to think about this as the greatest integer function, OK? We can draw a number line and think about it that way. And so we have negative six and moving to the right, negative five, negative four, negative three. And then moving to the left from negative six, we have negative seven, negative eight. OK? And that's just our number line around that point. Our point is at negative 5.8. So it's gonna be between negative five and negative six, a little bit closer to negative six. When we think of the greatest integer function, OK? It's the greatest integer less than the value we're at OK? When we have a number line and we want numbers that are less than we move to the left. OK? Numbers to the right are greater numbers to the left are less then so we take our value, we're gonna go to the left until we hit the first integer. In this case, that's negative six. And so our function becomes four minus and then this floor of negative 5.8 is negative six. OK? So we have four minus negative six. This is equivalent to four plus six and this gives us a value of 10. So if we look at our answer choices, we see that our function F evaluated at X equals 5.8 is going to be 10 which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

Find the value of the function for the given value of x. See Example 3. ƒ(x)=2-[[-x]], for x=3.7

Key Concepts

Function Evaluation

Floor Function (Greatest Integer Function)

Handling Negative Inputs in Floor Functions

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