Find the Domain of the Function $f ( x ) = \frac { 1 } { x ^ { 2 } + 5 x - 14 }$

question 97

Short Answer

Find the domain of the function.
- $f ( x ) = \frac { 1 } { x ^ { 2 } + 5 x - 14 }$
A) $\{ x \mid x \neq - 7 \text { and } x \neq 2 \} , \text { or } ( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty )$
B) $\{ x \mid x \neq - 7 \} \text {, or } ( - \infty , - 7 ) \cup ( - 7 , \infty )$
C) $\{ x \mid x \neq 2 \} , \text { or } ( - \infty , 2 ) \cup ( 2 , \infty )$
D) all real numbers, or $( - \infty , \infty )$

• A) \(\{ x \mid x \neq - 7 \text { and } x \neq 2 \} , \text { or } ( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty )\)
• B) \(\{ x \mid x \neq - 7 \} \text {, or } ( - \infty , - 7 ) \cup ( - 7 , \infty )\)
• C) \(\{ x \mid x \neq 2 \} , \text { or } ( - \infty , 2 ) \cup ( 2 , \infty )\)
• D) all real numbers, or \(( - \infty , \infty )\)

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Definitions:

Pupil

The central, circular opening in the iris of the eye, which regulates the amount of light that enters the eye to reach the retina.

Iris

The colored part of the eye surrounding the pupil, responsible for controlling the diameter and size of the pupil and thus the amount of light reaching the retina.

Visible Light Waves

Electromagnetic waves that are visible to the human eye, which perceive them as colors.

Pupil

The adjustable opening in the center of the eye that allows varying amounts of light to enter.