The domain of the function f(x) = ^ - 1 [ _2 (x/2)] is - Vidyadip

MCQ

The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is

✓
$[1, 4]$
B
$[-4, 1]$
C
$[-1, 4]$
D
None of these

✓

Answer

Correct option: A.

$[1, 4]$

a
(a) $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$, Domain of ${\sin ^{ - 1}}x$ is $x \in [ - 1,\,1]$

==> $ - 1 \le {\log _2}(x/2) \le 1$ ==> $\frac{1}{2} \le \frac{x}{2} \le 2$

==> $1 \le x \le 4$

$\therefore$ $x \in [1,\,4]$.

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