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/4]], for x=7

Accepted Answer

Hey, everyone. Welcome back. In this problem, we are asked to evaluate the value of the following function for X equals 11. And the function we're given is F of X is equal to the floor of X over six. And so this double square notation, square bracket notation indicates the floor function or the greatest integer function. Okay. It can be called both things. So you may have heard either term. So we have this function And we want to evaluate it at a particular x value and in this case of x value is x equals 11. So when we have a function, we want to evaluate it at a particular value, what we're gonna do is replace all of the X terms in our function with the value of interest. So we have F at 11. Okay. So this notation F in brackets 11 says F at 11. So it's the function F evaluated at the X value 11 And that is going to equal to the floor or greatest integer of divided by six. Alright. So before we figure out what the floor, the greatest integer is, we need to simplify what's in the brackets there. Okay. We want to have an idea of what this number actually is in terms of a decimal. And so if we write this out, we're going to have that 11 for six is 1. repeated. And so our function is equal to the floor of 1.83 repeated. Now, if you think of this function as the floor function, the floor, if you think of a floor in your house or in a building, the floor is underneath you, okay. It's on the bottom. And so the floor of a number is going to be the integer below, okay or less than. So in this case, we have 1.83, the number beneath that is one maybe integer beneath that is one. You can also think of this as a number line. So we draw a number line and we have 1234 K moving to the right. And then from one, we have zero negative, one negative two moving to the left. And our value of 1.83 is right between one and two. Okay. A little closer to two. Now, when we talk about this as the greatest integer function, it's the greatest integer less than the value we're at. Okay. So if we're at a particular value and we want a, an integer that is less, then we're gonna move to the left on our number line, moving to the left means getting numbers that are less than until we hit the first integer and that's going to be one. Okay. So either way you want to think about this, you're gonna get the same value. And in this case that is one. And so if we look at our answer choices, we see that we have answer choice. A, our function F evaluated X equals 11 is going to be one. 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/4]], for x=7

Key Concepts

Function Notation and Evaluation

Floor Function (Greatest Integer Function)

Order of Operations

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