what is the domain of the function f(x)=sin-1(log2(x2/2)) - Maths - Relations and Functions

Question

what is the domain of the function
f(x)=sin-1(log2(x2/2))

Shridhar Kaushik · Accepted Answer

We know that sinâ€“1x exists if $- 1 \leq x \leq 1 ∴ f (x) = \sin^{- 1} [\log_{2} (\frac{x^{2}}{2})] exists if - 1 \leq \log_{2} (\frac{x^{2}}{2}) \leq 1 \Rightarrow 2^{- 1} \leq \frac{x^{2}}{2} \leq 2^{1} [Taking base 2 to remove \log_{2}] \Rightarrow \frac{1}{2} \leq \frac{x^{2}}{2} \leq 2 \Rightarrow \frac{1}{2} \times 2 \leq \frac{x^{2}}{2} \times 2 \leq 2 \times 2 [Multiplying by 2] \Rightarrow 1 \leq x^{2} \leq 4 \Rightarrow 1 \leq x \leq 2 or - 2 \leq x \leq - 1$ Hence, the domain of f(x) is $[- 2, - 1] \cup [1, 2]$

what is the domain of the function f(x)=sin-1(log2(x2/2)).

what is the domain of the function f(x)=sin^-1(log₂(x²/2)).