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Find all vertical asymptotes of the function f(x) = (3x² - 14x + 16) / (2x² - 10x + 12)?

User Asli
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Final answer:

To find the vertical asymptotes of the function f(x) = (3x² - 14x + 16) / (2x² - 10x + 12), we need to determine the values of x where the denominator of the function is equal to zero. The vertical asymptotes are x = 3 and x = 2.

Step-by-step explanation:

To find the vertical asymptotes of the function f(x) = (3x² - 14x + 16) / (2x² - 10x + 12), we need to determine the values of x where the denominator of the function is equal to zero. The denominator is a quadratic equation of the form ax² + bx + c = 0, where a = 2, b = -10, and c = 12. We can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c into the quadratic formula, we get:

x = (-(-10) ± √((-10)² - 4(2)(12))) / (2(2))

x = (10 ± √(100 - 96)) / 4

x = (10 ± √4) / 4

x = (10 ± 2) / 4

Therefore, the values of x are:

x = (10 + 2) / 4 = 12 / 4 = 3

x = (10 - 2) / 4 = 8 / 4 = 2

So, the vertical asymptotes of the function f(x) = (3x² - 14x + 16) / (2x² - 10x + 12) are x = 3 and x = 2.

User Isaac Kleinman
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