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Direction Cosines

Find the doma...

Question

Find the domain of definition of the following function:
$y = \sqrt{{log}_{0.3} (x^{2} - 5 x + 7)}$

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Solution

${log}_{0.3} (x^{2} - 5 x + 7) \geq 0$
As the base is less than $1$
$0 < (x^{2} - 5 x + 7) \leq 1$
Solving inequalities we get
$x^{2} - 5 x + 7 > 0 f o r a l l x \in R$ and $x^{2} - 5 x + 7 \leq 1 x^{2} - 5 x + 6 \leq 0 (x - 3) (x - 2) \leq 0 x \in [2, 3]$
Taking intersection, we get
$x \in [2, 3]$

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