Pergunta

4. Select one of the following that best describes the domain of g(x)=(2x^2+18x-44)/(x^2)+8x+15 a. xvert xneq 3,5 b. xvert xneq -3,-5 c. xvert xneq 2,-11 d. xvert xneq -2,11
Solução

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MaxelineMestre · Tutor por 5 anos
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To determine the domain of the function $g(x)=\frac {2x^{2}+18x-44}{x^{2}+8x+15}$, we need to find the values of $x$ for which the denominator is not equal to zero.<br /><br />The denominator of the function is $x^{2}+8x+15$. To find the values of $x$ that make the denominator zero, we can factor the quadratic expression:<br /><br />$x^{2}+8x+15 = (x+3)(x+5)$<br /><br />Setting each factor equal to zero, we get:<br /><br />$x+3=0$ or $x+5=0$<br /><br />Solving for $x$, we find:<br /><br />$x=-3$ or $x=-5$<br /><br />Therefore, the domain of the function $g(x)$ is all real numbers except $x=-3$ and $x=-5$. In set notation, this can be written as:<br /><br />$\{ x\vert x\neq -3,-5\}$<br /><br />So, the correct answer is option b. $\{ x\vert x\neq -3,-5\}$.
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