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Question: \(f(x) = \frac{\log_{2}(x + 3)}{x^{2} + 3x + 2}( - 3,\infty)\) equals to –...

f(x)=log⁡2(x+3)x2+3x+2(−3,∞)f(x) = \frac{\log_{2}(x + 3)}{x^{2} + 3x + 2}( - 3,\infty) equals to –

A

– {−1,−2}\{ - 1, - 2\}

B

(−3,∞)−{−1,−2}( - 3,\infty) - \{ - 1, - 2\}

C

–(−∞,∞)( - \infty,\infty)

D

f(x)=(2−2x−x2)f(x) = \sqrt{(2 - 2x - x^{2})}

Answer

– {−1,−2}\{ - 1, - 2\}

Explanation

Solution

lim⁡x→2\lim _ { x \rightarrow 2 } (4x2−4−1x−2)\left( \frac { 4 } { x ^ { 2 } - 4 } - \frac { 1 } { x - 2 } \right) = lim⁡x→2\lim _ { x \rightarrow 2 } (4−x−2x2−4)\left( \frac { 4 - x - 2 } { x ^ { 2 } - 4 } \right)

=lim⁡x→2\lim _ { x \rightarrow 2 } = −14\frac { - 1 } { 4 }