Domain of the function f(x)= ⁻¹(2 x)+ 6 for real valued of x is

Step-by-step solution

For the function f(x) = ⁻¹(2x) + 6 to be defined, the expression inside the square root must be non-negative: ⁻¹(2x) + 6 0 ⁻¹(2x) - 6 Taking the sine of both sides, since (x) is an increasing function on its domain [- /2, /2] : 2x (- 6 ) 2x - 1 2 x - 1 4 Additionally, the domain of ⁻¹(u) is u [-1, 1] . Therefore, for ⁻¹(2x) to be defined: -1 2x 1 - 1 2 x 1 2 Combining the two conditions x - 1 4 and - 1 2 x 1 2 , we get: - 1 4 x 1 2 Answer: [ array ll - 1 4 , & 1 2 array ]