Domain of the function f(x)= sin -1( log 2x) in the set of real numbers is:

Question

Domain of the function f(x)= sin -1( log 2x) in the set of real numbers is: (A)  x:1 le x le 2  (B)  x:1 le x le 3  (C)  x:-1 le x le 2  (D)  x:(1/2) le x le 2

Tardigrade Admin · Accepted Answer

We have, f(x)= sin -1( log 2x) ∴ -1 le log 2x le 1 (∵ -1 le sin -1x le 1) ⇒ 2-1 le x le 21 ⇒ (1/2) le x le 2 ∴ Domain of the function = x:(1/2) le x le 2

Q. Domain of the function $f (x) = sin^{- 1} (lo g_{2} x)$ in the set of real numbers is:

${x : 1 \leq x \leq 2}$

${x : 1 \leq x \leq 3}$

${x : - 1 \leq x \leq 2}$

${x : \frac{1}{2} \leq x \leq 2}$

${x : - \frac{1}{2} \leq x \leq 2}$

We have, $f (x) = sin^{- 1} (lo g_{2} x)$ $∴$ $- 1 \leq lo g_{2} x \leq 1$ $(∵ - 1 \leq sin^{- 1} x \leq 1)$ $\Rightarrow$ $2^{- 1} \leq x \leq 2^{1}$ $\Rightarrow$ $\frac{1}{2} \leq x \leq 2$ $∴$ Domain of the function $= {x : \frac{1}{2} \leq x \leq 2}$

Q. Domain of the function f(x)=sin−1(log2​x) in the set of real numbers is:

{x:1≤x≤2}

{x:1≤x≤3}

{x:−1≤x≤2}

{x:21​≤x≤2}

{x:−21​≤x≤2}

We have, f(x)=sin−1(log2​x) ∴ −1≤log2​x≤1 (∵−1≤sin−1x≤1) ⇒ 2−1≤x≤21 ⇒ 21​≤x≤2 ∴ Domain of the function ={x:21​≤x≤2}