First slide

Functions (XII)

Question

Find the domain of the function $f (x) = \sqrt{\frac{1}{| x - 2 | - (x - 2)}}$

Easy

A

$(- \infty, 2)$
B

$(- \infty, - 2)$
C

$(- \infty, 2]$
D

$(- \infty, - 2]$

Solution

$\begin{array}{l} | x - 2 | = \{\begin{cases} x - 2, & x \geq 2 \\ 2 - x, & x < 2 \end{cases} \\ \Rightarrow | x - 2 | - (x - 2) = \{\begin{matrix} 0, x \geq 2 \\ 4 - 2 x, x < 2 \end{matrix} \\ \Rightarrow given expression is defined for (- \infty, 2) \end{array}$

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