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

Question

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

Answer 1

Since for , $0 < a < 1$ , $\log_{a}x < 0$ for $x > 1$ so

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

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