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Absolute Value Function

If |x2+3x-4| ...

Question

If $| x^{2} + 3 x - 4 | = | x + 4 |$ , then $x =$

A

- 4

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B

2

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C

- 2

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D

0

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Solution

The correct option is D $0$
$| x^{2} + 3 x - 4 | = | x + 4 | \Rightarrow (| x + 4 |) (| x - 1 |) = | x + 4 | \Rightarrow (| x + 4 |) (| x - 1 | - 1) = 0 \Rightarrow | x - 1 | = 1 or | x + 4 | = 0 \Rightarrow x - 1 = \pm 1 or x + 4 = 0 \Rightarrow x = 2, 0, - 4$

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| x^{2} + 3 x - 4 | = | x + 4 |

x =

x

y = \frac{x^{2} - 3 x + 4}{x^{2} + 3 x + 4}

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, then what is the value of

x^{2} + 3 x - 4

x

is real, then the value of

\frac{x^{2} - 3 x + 4}{x^{2} + 3 x + 4}

lies in the interval

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