What is the domain and range of $\sqrt{\frac{5 x + 6}{2}}$ $sqrt((5x+6)/2)$ ?

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What is the domain and range of $\sqrt{\frac{5 x + 6}{2}}$ $sqrt((5x+6)/2)$ ?

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Answer 1 · 2016-03-15T01:48:27

Answer:

Domain $x \in [- \frac{6}{5}, \infty)$ $x in[-6/5,oo)$
Range $[0, \infty)$ $[0,oo)$

Explanation:

You must keep in mind that for the domain:

$\sqrt{y} \to y \geq 0$ $sqrt(y)->y>=0$

$ln (y) \to y > 0$ $ln(y)->y>0$

$\frac{1}{y} \to y \neq 0$ $1/y->y!=0$

After that, you will be lead to an unequality giving you the domain.

This function is a combination of linear and square functions. Linear has domain $RR$ . The square function though must have a positive number inside the square. Therefore:

$(5x+6)/2>=0$

Since 2 is positive:

$5x+6>=0$

$5x>= -6$

Since 5 is positive:

$x>= -6/5$

The domain of the functions is:

$x in[-6/5,oo)$

The range of the root function (outer function) is $[0,oo)$ (infinite part can be proven through the limit as $x->oo$ ).

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What is the domain and range of $\sqrt{\frac{5 x + 6}{2}}$ $sqrt((5x+6)/2)$ ?

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Explanation:

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