Chapter 6.3, Problem 49HP

To determine

Write a square root function for which the domain is $\left\{x\right|x\ge 8\}$ and the range is $\left\{y\right|y\le 14\}$ .

Answer to Problem 49HP

  $f(x)=14-\sqrt{x-8}$

Explanation of Solution

Given:

Domain = $\left\{x\right|x\ge 8\}$

Range = $\left\{y\right|y\le 14\}$

Calculation:

Since the domain is $[8,\infty ]$ , so the vertex is shifted from origin to x = 8.

Hence , the function must contain $\sqrt{x-8}$ as the principal function $y=\sqrt{x}$ is shifted 8 units to the right.

Since the range is $(-\infty ,14]$ , we are dealing with the principal function $y=-\sqrt{x}$ , since it goes towards $-\infty$ .

So, we will now include the expression $-\sqrt{x-8}$ and since the principal function is shifted 14 units upward , the function is :

  $y=14-\sqrt{x-8}$

So, the required equation for square root function is $f(x)=14-\sqrt{x-8}$