f(x)= [[x]]
The function you provided, f(x) = [[x]], is known as the floor function
The function you provided, f(x) = [[x]], is known as the floor function. The double brackets around x represent the greatest integer less than or equal to x. In other words, the floor function rounds down any real number x to the nearest integer less than or equal to x.
To understand how this function works, let’s consider a few examples:
Example 1:
Let’s evaluate f(3.7). Since 3.7 is between 3 and 4, the greatest integer less than or equal to 3.7 is 3. Therefore, f(3.7) = 3.
Example 2:
Now let’s evaluate f(-2.3). Since -2.3 is between -3 and -2, the greatest integer less than or equal to -2.3 is -3. Therefore, f(-2.3) = -3.
Example 3:
To further illustrate, let’s evaluate f(5). In this case, 5 is an integer itself. So, the greatest integer less than or equal to 5 is 5. Therefore, f(5) = 5.
Example 4:
Finally, let’s evaluate f(pi). Pi is approximately 3.14159, and since pi is between 3 and 4, the greatest integer less than or equal to pi is 3. Therefore, f(pi) = 3.
In summary, the floor function, f(x) = [[x]], rounds down any real number x to the nearest integer less than or equal to x.
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