Q. 46 - Precalculus Enhanced with Graphing Utilities

Question

If  $f\left(x\right)=int\left(\frac{x}{2}\right)$, find

1. $f(1.2)$
   
2. $f(1.6)$
   
3. $f(-1.8)$
   

Step-by-Step Solution

Answer

1. The value of $f(1.2)$ is $0$.
2. The value of $f(1.6)$ is $0$ .
3. The value of $f(-1.8)$ is $-1$.

Step 1. Given Information

We are given a function, 

$f\left(x\right)=int\left(\frac{x}{2}\right)$

The greatest integer function gives the integer less than or equal to the given number. 

Part(a) Step 1. Finding part(a)

Putting $x=1.2$ in the given function, we get

$$\begin{gathered} f\left(x\right)=int\left(\frac{x}{2}\right) \\ f(1.2)=int\left(\frac{1.2}{2}\right) \\ f(1.2)=int\left(0.6\right) \end{gathered}$$

The greatest integer less than $1.2$ is $0$, so 

$f(1.2)=0$

Part(b) Step 1. Finding part(b)

Putting $x=1.6$  in the given function, we get

$$\begin{gathered} f\left(x\right)=int\left(\frac{x}{2}\right) \\ f(1.6)=int\left(\frac{1.6}{2}\right) \\ f(1.6)=int\left(0.8\right) \end{gathered}$$

The greatest integer less than $0.8$ is $0$, so

$f(1.6)=0$

Part(c) Step 1. Finding part(c)

Putting $x=-1.8$  in the given function, we get

$$\begin{gathered} f\left(x\right)=int\left(\frac{x}{2}\right) \\ f(-1.8)=int\left(\frac{-1.8}{2}\right) \\ f(-1.8)=int\left(-0.9\right) \end{gathered}$$

The greatest integer less than $-0.9$ is $-1$, so 

$f(-1.8)=-1$