Consider the real-valued function satisfying 2f(sin⁡x)+f(cos⁡x)=x. Then, which of the following is not true?

Given 2f(sin⁡x)+f(cos⁡x)=x-----(1) Replace x by π2−x, we have 2f(cos⁡x)+f(sin⁡x)=π2−x   ------(2) Eliminating f(cos⁡x) from (1) and (2), we have f(sin⁡x)=x−π6⇒ f(x)=sin−1⁡x−π6 Then, domain of f(x) is [−1,1] .  Range is −π2−π6,π2−π6 or −2π3,π3 Also, f(x) is one-one.