First slide

Functions (XII)

Question

The domain of $f (x) = \log_{10} \frac{x - 5}{x^{2} - 10 x + 24} - \sqrt[3]{x + 5}$ is

Moderate

A

(4, 5)
B

$(6, \infty)$
C

$(4, 5) \cup (6, \infty)$
D

$(4, 5] \cup (6, \infty)$

Solution

$\log_{10} \frac{x - 5}{x^{2} - 10 x + 24}$ is defined then $\frac{x - 5}{x^{2} - 10 x + 24} > 0$ $(x - 4) (x - 5) (x - 6) > 0$

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