Find the domain of the following functions :
(a) $y = 1 - {log}_{10} x$
(b) $y = \frac{1}{\sqrt{x^{2} - 4 x}}$

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Solution

$(a) y = 1 - {log}_{10} x ⟹ x > 0$
So the domain is $x \in (0, \infty)$
$(b) y = \frac{1}{\sqrt{x^{2} - 4 x}} ⟹ x^{2} - 4 x > 0$
$⟹ x (x - 4) > 0 ⟹ x \in (- \infty, 0) \cup (4, \infty)$

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