The range of f(x) = frac{x^2 + 34x - 71}{x^2 | vedclass

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(B) Let $y = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$.$y(x^2 + 2x - 7) = x^2 + 34x - 71$$x^2(y - 1) + x(2y - 34) - 7y + 71 = 0$.For $x$ to be real,the dis

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$( - \infty, 5] \cup [9, \infty)$

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(B) Let $y = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$.$y(x^2 + 2x - 7) = x^2 + 34x - 71$$x^2(y - 1) + x(2y - 34) - 7y + 71 = 0$.For $x$ to be real,the discriminant $D \ge 0$:$D = (2y - 34)^2 - 4(y - 1)(-7y + 71) \ge 0$$4(y - 17)^2 - 4(-7y^2 + 71y + 7y - 71) \ge 0$$(y^2 - 34y + 289) - (-7y^2 + 78y - 71) \ge 0$$8y^2 - 112y + 360 \ge 0$$y^2 - 14y + 45 \ge 0$$(y - 5)(y - 9) \ge 0$.Thus,$y \le 5$ or $y \ge 9$.The range is $( - \infty, 5] \cup [9, \infty)$.

The range of $f(x) = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$ is

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