Chapter 10, Problem 1RP

To determine

To calculate: The value of $f\left(a-1\right)$ for the function, $f\left(x\right)=\frac{1}{2}x+3$.

Answer to Problem 1RP

Solution:

The value for the function $f\left(x\right)=\frac{1}{2}x+3$ is $\underset{\_}{f\left(a-1\right)=\frac{a}{2}+\frac{5}{2}}$.

Explanation of Solution

Given:

A function as,

$f\left(x\right)=\frac{1}{2}x+3$

Calculation:

Consider the following function.

$f\left(x\right)=\frac{1}{2}x+3$,

Substitute $\left(a-1\right)$ for x.

$\begin{array}{ccc}\hfill f\left(a-1\right)& =& \frac{1}{2}\left(a-1\right)+3\hfill \\ \hfill & =& \frac{1}{2}a-\frac{1}{2}+3\hfill \\ \hfill & =& \frac{a}{2}+\frac{6}{2}-\frac{1}{2}\hfill \\ \hfill & =& \frac{a}{2}+\frac{5}{2}\hfill \end{array}$

Hence, the value is $f\left(a-1\right)=\frac{a}{2}+\frac{5}{2}$.