I try this question number of times but i can’t solve it.please explain this question by solving

OK lets see
Domain:
Domain is the values of the x which f(x) can take to yield a meaningful answer. The only problamatic function is the underoot function which enforces the condition

as
the condition is always true and hence the domain of f(x) is the whole real line!

Range:
This one is simple, again as the sine function stays between -1 and 1 we need to compute f(x) when sin(x) = -1 and when sin(a) = 1
for sin(x) = -1, f(x) = 1 and when sin(x) = 1, f(x) = 1/sqrt{7}
Thus the range is