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)=[[3-(x/2)]], for x=1

Accepted Answer

Everyone. In this problem, we are asked to evaluate the value of the following function for X equals two. And the function we're given is F of X is equal to the floor of four minus X over four. Okay. So these double square brackets indicate the floor function or it's sometimes called the greatest integer function. You may have heard either of those terms. So when we have a function F of X is equal to the greatest integer of four minus X over four and were asked to evaluate it at a specific X value. In this case, X equals to what we're gonna do is take that function. And everywhere we have an X, we're gonna replace that with our X value. And so we have F F two is equal to. And this two notation tells us our function evaluated at the X value to Okay. On the right hand side, we get 4 -2 divided by four, just like with regular brackets. We want to evaluate what's inside of this floor or greatest integer function before we evaluate it. And so we simplify in the brackets, we have four minus 2/4. We can simplify 2/4 to B minus at half, four, minus a half, gives us 3.5. And now we want to take the floor of 3.5. Okay? or the greatest integer less than 3.5. Okay. So if you want to think about it as a floor, Okay, you're thinking about the bottom. Okay. So the bottom Below 3.5, the next integer is going to be three. Okay? Or you can think of it as the greatest integer less than if we draw a number line. Imagine We have three, 456 K moving to the right on our number line and then we have from three, we have two and one moving to the left and our value is 3.5. So it's gonna be right between three and four and the greatest integer lesson. Okay. Well, an intruder lesson if we have a number line and we're talking about lesson the numbers to the left of the value we're at are going to be less than the value that we're currently at. Okay. So we're going to move to the left until we hit the first integer and that's going to be three. And so our floor function or the greatest integer of 3.5 is going to be three, then that's our solution. So the function F evaluated at the X value two is going to be three and that 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)=[[3-(x/2)]], for x=1

Key Concepts

Function Notation

Substitution

Order of Operations

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