For what values of $x$ will the expression represent a real number?
Write answers using inequality notation.
$\sqrt{\frac{x + 7}{3 - x}}$

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Solution

$\sqrt{\frac{x + 7}{3 - x}}$

$D o m a i n o f \sqrt{\frac{x + 7}{3 - x}} : [\begin{matrix} S o l u t i o n : & - 7 \leq x < 3 I n t e r v a l N o t a t i o n : & [- 7, 3) \end{matrix}]$

$R a n g e o f \sqrt{\frac{x + 7}{3 - x}} : [\begin{matrix} S o l u t i o n : & f (x) \geq 0 I n t e r v a l N o t a t i o n : & [0, \infty) \end{matrix}]$

$T a k e t h e d e n o m i n a t o r (s) o f \sqrt{\frac{x + 7}{3 - x}} a n d c o m p a r e t o z e r o$

$x = 3$

$E x t r e m e P o i n t s o f \sqrt{\frac{x + 7}{3 - x}} : M i n i m u m (- 7, 0)$

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