Q. 45 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

1. The value of $f(1.2)$ is $2$ .
2. The value of $f(1.6)$ is $3$ .
3. The value of $f(-1.8)$ is $-4$ .

Step 1. Given Information

We are given a function,

$f\left(x\right)=int\left(2x\right)$

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

$$\begin{gathered} f\left(x\right)=int\left(2x\right) \\ f(1.2)=int\left(2\right(1.2\left)\right) \\ f(1.2)=int(2.4) \end{gathered}$$

The greatest integer less than $2.4$ is $2$, so

$f(1.2)=2$

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

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

$$\begin{gathered} f\left(x\right)=int\left(2x\right) \\ f(1.6)=int\left(2\right(1.6\left)\right) \\ f(1.6)=int(3.2) \end{gathered}$$

The greatest integer less than  $3.2$ is $3$, so

$f(1.6)=3$

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

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

$$\begin{gathered} f\left(x\right)=int\left(2x\right) \\ f(-1.8)=int\left(2\right(-1.8\left)\right) \\ f(-1.8)=int(-3.6) \end{gathered}$$

The greatest integer less than $-3.6$ is $-4$, so

$f(-1.8)=-4$