Math  /  Calculus

QuestionQuestion 9 Not yet answered fligg quartion
If f(x)={x2xx21 if x>12k3 if x1f(x)=\left\{\begin{array}{ll}\frac{x^{2}-x}{x^{2}-1} & \text { if } x>1 \\ 2 k-3 & \text { if } x \leq 1\end{array}\right. is continuous at x=1x=1, then k=k= 12\frac{1}{2} 34\frac{3}{4} 1 74\frac{7}{4} 74\frac{-7}{4}

Studdy Solution
مساواة النهايتين للحصول على قيمة k k :
12=2k3 \frac{1}{2} = 2k - 3
حل المعادلة:
2k3=12 2k - 3 = \frac{1}{2} 2k=12+3 2k = \frac{1}{2} + 3 2k=12+62 2k = \frac{1}{2} + \frac{6}{2} 2k=72 2k = \frac{7}{2} k=74 k = \frac{7}{4}
قيمة k k هي:
74 \boxed{\frac{7}{4}}

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