For what values of $x$ will the expression represent a real number? Write answers using inequality notation. $\sqrt{\frac{x - 1}{x + 3}}$

Open in App

Solution

$\sqrt{\frac{x - 1}{x + 3}}$

$D o m a i n o f \sqrt{\frac{x - 1}{x + 3}} : [\begin{matrix} S o l u t i o n : & x < - 3 o r x \geq 1 I n t e r v a l N o t a t i o n : & (- \infty, - 3) \cup [1, \infty) \end{matrix}]$

$R a n g e o f \sqrt{\frac{x - 1}{x + 3}} : [\begin{matrix} S o l u t i o n : & 0 \leq f (x) < 1 o r f (x) > 1 I n t e r v a l N o t a t i o n : & [0, 1) \cup (1, \infty) \end{matrix}]$

Take denominator equal to zero $x + 3 = 0 \Rightarrow x = - 3$

$E x t r e m e P o i n t s o f \sqrt{\frac{x - 1}{x + 3}} : M i n i m u m (1, 0)$

Suggest Corrections

Similar questions

x

\sqrt{2 x^{2} + x - 6}

x

\sqrt{3 x^{2} - 7 x - 6}

\frac{x + 3}{x - 3} \geq 0

x^{2} + x < 12

x + x + x + x

Join BYJU'S Learning Program