The domain of f(x) = sin-1 [Log2 ( (x /2))] is

Question

The domain of f(x) = sin-1 [Log2 ( (x /2))] is (A) 0 ≤ x ≤ 1 (B) 0 ≤ x ≤ 4 (C) 1 ≤ x ≤ 4 (D) 4 ≤ x ≤ 6

Tardigrade Admin · Accepted Answer

Given function, f(x)= sin -1[ log 2((x/2))] Since, -1 ≤ sin x ≤-1 ⇒ -1 ≤ log 2((x/2)) ≤ 1 ⇒ 2-1 ≤ x / 2 ≤ 21 ⇒ 20 ≤ x ≤ 22 ⇒ 1 ≤ x ≤ 4 Required domain is x ∈[1,4].

Q. The domain of $f (x) = s i n^{- 1} [L o g_{2} (\frac{x}{2})]$ is

$0 \leq x \leq 1$

$0 \leq x \leq 4$

$1 \leq x \leq 4$

$4 \leq x \leq 6$

Given function, $f (x) = sin^{- 1} [lo g_{2} (\frac{x}{2})]$
Since, $- 1 \leq sin x \leq - 1$
$\Rightarrow - 1 \leq lo g_{2} (\frac{x}{2}) \leq 1$
$\Rightarrow 2^{- 1} \leq x /2 \leq 2^{1}$
$\Rightarrow 2^{0} \leq x \leq 2^{2}$
$\Rightarrow 1 \leq x \leq 4$
Required domain is $x \in [1, 4] .$

Q. The domain of f(x)=sin−1[Log2​(2x​)] is

0≤x≤1

0≤x≤4

1≤x≤4

4≤x≤6