Chapter 9, Problem 10PFA

To determine

To select correct domain from the given options.

Answer to Problem 10PFA

Option D. $\left\{x\right|x>-2\}$

Explanation of Solution

Given information :

The function provided is $y=-2x+1$ .

Range provided is $\left\{y\right|y<5\}$

Option A. $\left\{x\right|x<2\}$

Option B. $\left\{x\right|x>2\}$

Option C. $\left\{x\right|x<-2\}$

Option D. $\left\{x\right|x>-2\}$

Option A. $\left\{x\right|x<2\}$

  $y=-2x+1$

Substituting $x=-4$ which falls under $\left\{x\right|x<2\}$ in the expression,

  $y=-2(-4)+1$

Simplifying.

  $y=9$

Hence, option A. is rejected as $y=9$ is beyond the given range $\left\{y\right|y<5\}$

Option B. $\left\{x\right|x>2\}$

  $y=-2x+1$

Substituting $x=3$ which falls under $\left\{x\right|x>2\}$ in the expression,

  $y=-2(3)+1$

Simplifying.

  $y=-5$

Hence, option B. is rejected as $y=-5$ as it is maximum value it can take have.

Option C. $\left\{x\right|x<-2\}$

  $y=-2x+1$

Substituting $x=-4$ which falls under $\left\{x\right|x<-2\}$ in the expression,

  $y=-2(-4)+1$

Simplifying.

  $y=9$

Hence, option C. is rejected as $y=9$ is beyond the given range $\left\{y\right|y<5\}$

Option D. $\left\{x\right|x>-2\}$

  $y=-2x+1$

Substituting $x=-1$ which falls under $\left\{x\right|x>-2\}$ in the expression,

  $y=-2(-1)+1$

Simplifying.

  $y=3$

Hence, option D. is accepted as $y=3$ in the range $\left\{y\right|y<5\}$