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Strictly Increasing Functions

Find the doma...

Question

Find the domains of definition of the following function:

$y = (x + 0.5)^{log (0.5 + x) \frac{x^{2} + 2 x - 3}{4 x^{2} + 4 x - 3}} .$

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Solution

$x + 0.5 > 0 ⟹ x > - 0.5$

$4 x^{2} + 4 x - 3 \neq 0 ⟹ x \neq 2, - 6$

$\frac{x^{2} + 2 x - 3}{4 x^{2} + 4 x - 3} > 0$

$3 x^{2} + 2 x < 0 ⟹ x \in (- 2 / 3, 0)$

$x \in (- 2 / 3, 0)$

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Strictly Increasing Functions

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