Question

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

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

Short 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-by-step solution

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

localid="1645893962967" $$\begin{gathered} f\left(x\right)=int\left(\frac{x}{2}\right) \\ f(1.6)=int\left(\frac{1.6}{2}\right) \\ f(1.6)=int\left(0.8\right) \end{gathered}$$

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

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

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

$f(-1.8)=-1$