First slide

Functions (XII)

Question

The domain of the function $f (x) = \frac{1}{\sqrt{4 x - |x^{2} - 10 x + 9|}}$ is

Difficult

A

$(7 - \sqrt{40}, 7 + \sqrt{40})$
B

$(0, 7 + \sqrt{40})$
C

$(7 - \sqrt{40}, \infty)$
D

none of these

Solution

$\begin{array}{l} f (x) = \frac{1}{\sqrt{4 x - |x^{2} - 10 x + 9|}} \\ For f (x) to be defined, |x^{2} - 10 x + 9| < 4 x \\ or x^{2} - 10 x + 9 < 4 x and x^{2} - 10 x + 9 > - 4 x \\ or x^{2} - 14 x + 9 < 0 and x^{2} - 6 x + 9 > 0 \\ or x \in (7 - \sqrt{40,} 7 + \sqrt{40}) and x \in R - \{3\} \\ or x \in (7 - \sqrt{40}, 3) \cup (3, 7 + \sqrt{40}) \end{array}$

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