1.2 If $$ f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} $$, for which values of $$ x $$ is $$ \begin{array}{ll}1.2 .2 & f(x) ext { non real. } \ 1.2 .3 & f(x) ext { undefined } \ 1.2 .4 & f(x)0\end{array} $$

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1.2 If $$ f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} $$, for which values of $$ x $$ is $$ \begin{array}{ll}1.2 .2 & f(x) 	ext { non real. } \ 1.2 .3 & f(x) 	ext { undefined } \ 1.2 .4 & f(x)>0\end{array} $$

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Let's analyze the function $$ f(x) = \frac{\sqrt{x + 2}}{3 - 3x^{2}} $$ to determine the conditions for each part of the problem. ### 1.2.2 **Values of $$ x $$ for which $$ f(x) $$ is Non-Real** For $$ f(x) $$ to be real, the expression under the square root must be non-negative: $$ x + 2 \geq 0 \implies x \geq -2 $$ Therefore, $$ f(x) $$ is **non-real** when: $$ x < -2 $$ ### 1.2.3 **Values of $$ x $$ for which $$ f(x) $$ is Undefined** The function $$ f(x) $$ is undefined when the denominator is zero: $$ 3 - 3x^{2} = 0 \implies 1 - x^{2} = 0 \implies x^{2} = 1 \implies x = \pm 1 $$ Therefore, $$ f(x) $$ is **undefined** at: $$ x = 1 \quad \text{and} \quad x = -1 $$ ### 1.2.4 **Values of $$ x $$ for which $$ f(x) > 0 $$** For $$ f(x) $$ to be positive: 1. The square root $$ \sqrt{x + 2} $$ must be positive, which requires: $$ x + 2 > 0 \implies x > -2 $$ 2. The denominator $$ 3 - 3x^{2} $$ must be positive: $$ 3 - 3x^{2} > 0 \implies 1 - x^{2} > 0 \implies |x| < 1 $$ Combining these two conditions: $$ -2 < x < 1 $$ However, we must exclude $$ x = -1 $$ and $$ x = 1 $$ because the function is undefined at these points. Since $$ x = 1 $$ is already excluded by $$ x < 1 $$, we only need to exclude $$ x = -1 $$. Therefore, $$ f(x) > 0 $$ for: $$ -2 < x < 1 \quad \text{and} \quad x \neq -1 $$ ### **Summary of Results** 1. **Non-Real Values:** $$ x < -2 $$ 2. **Undefined Values:** $$ x = 1 $$ and $$ x = -1 $$ 3. **Positive Values:** $$ -2 < x < 1 $$ with $$ x \neq -1 $$ - **Non-Real:** $$ x < -2 $$ - **Undefined:** $$ x = 1 $$ and $$ x = -1 $$ - **Positive:** $$ -2 < x < 1 $$ excluding $$ x = -1 $$

1.2 If , for which values of is

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