Chapter 3.9, Problem 1OE

To determine

To Find: The missing entries in the table.

Answer to Problem 1OE

The answer is 7 and 10.

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

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

So, the required function is $f(x)=3x-2$

Now,

  $\begin{array}{l}\text{when}x=3\\ f(x)=3\times 3-2\\ f(x)=9-2\\ f(x)=7\\ \text{and}\text{when}x=4\\ f(x)=3\times 4-2\\ f(x)=12-2\\ f(x)=10\end{array}$

Thus, the missing values are 7 and 10.