Question

Which domain restrictions apply to the rational expression? 14–2x / x^2–7x

Answer 1

3.
`\displaystyle 1(1)/(3) = x`

2C.
`\displaystyle III.`

2B.
`\displaystyle I.`

2A.
`\displaystyle II.`

1.
`\displaystyle Set-Builder\:Notation: x \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)`

Explanation:

3. See above.

2C. The keyword is ratio, which signifies division, so you would choose "III.".

2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2A. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

`\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: x \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)`

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Answer 2

\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]

Explanation:

Given expression is \[14 - 2x / x^{2} - 7x\]

For this rational expression to be valid it must satisfy the constraint that the denominator is not equal to 0.

This implies that \[x^{2} - 7x = 0\] should be false.

In order words \[x*(x-7) = 0\] should be false.

Or, x=0, x=7 must be false.

Hence the domain restriction that applies is as follows :

\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]