First slide

Functions (XII)

Question

The domain of the function
$f (x) = \frac{\sqrt{- \log_{0.3} (x - 1)}}{\sqrt{- x^{2} + 2 x + 8}}$ is

Moderate

A

$(1, 4)$
B

$(- 2, 4)$
C

$(2, 4)$
D

none of these

Solution

Since for, $0 < a < 1, \log_{a} x < 0$ for $x > 1$
so $\log_{0.3} (x - 1) < 0$ for $x > 2$ Also $- x^{2} + 2 x + 8 > 0$ if
and only if $x \in (- 2, 4)$ Hence the domain of the given. function is $(2, 4) .$

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