Chapter 7.6, Problem 43PPS

To determine

To determine the value of n

Answer to Problem 43PPS

  $n=3$

Explanation of Solution

Given:

  

Also, $f(x)={\left(\frac{1}{2}\right)}^x$

Calculation:

We have,

  $\begin{array}{l}\Rightarrow g(x)=f(x)+n\\ \Rightarrow g(x)={\left(\frac{1}{2}\right)}^x+n\mathrm{....................}(i)\end{array}$

Now, from the given graph it is clear that at $x=0$ , $y=4$ which means, $g(0)=4$ .

Therefore, putting $x=0$ in equation ( i ),

  $\begin{array}{l}\Rightarrow g(0)={\left(\frac{1}{2}\right)}^0+n\\ \Rightarrow 4=1+n\\ \Rightarrow n=3\end{array}$

Hence, The function becomes: $g(x)={\left(\frac{1}{2}\right)}^x+3$ .

Verification:

Using graphing utility tool the graph is plotted and compared with the given graph side by side.

(i(ii)

Interpretation:

When both the above graphs are compared it is clear that they are same, which means the calculations done are correct.

Conclusion:

Hence, $n=3$ .