Chapter 3.9, Problem 4OE

To determine

To Find: The missing entries in the table.

Answer to Problem 4OE

The answer is 3 and 5.

Explanation of Solution

Given information: Given values is a linear function.

Calculation:

Let the given linear function is $f(x)=ax+b$

From the table, we get

  $\begin{array}{l}\text{when}x=2\text{we}\text{get}f(x)=-1\text{put}\text{these}\text{values}\text{on}\text{the}\text{above}\text{function}\\ -1=a\times 2+b\\ 2a+b=-1\mathrm{...}(1)\\ \text{Similarly,}\\ \text{when}x=4\text{we}\text{get}f(x)=1,\text{than}\\ 1=a\times 4+b\\ 4a+b=1\mathrm{...}(2)\\ \text{From}(1),\text{we}\text{get}\\ b=-1-2a\\ 4a+(-1-2a)=1\\ 2a-1=1\\ 2a=1+1\\ 2a=2\\ a=1\text{and}\\ b=-1-2\times 1\\ b=-1-2\\ b=-3\end{array}$

So, the required function is $f(x)=x-3$

Now,

  $\begin{array}{l}\text{when}x=6\\ f(x)=6-3\\ f(x)=3\\ \text{and}\text{when}x=8\\ f(x)=8-3\\ f(x)=5\end{array}$

Thus, the missing values are 3 and 5.