Find the domain of each of the following function: `f(x)=sqrt(1-2x)+3sin^(-1)((3x-1)/2)`

Options

A. `[-1//3,1]`
B. `(-oo,1//2]`
C. `[-1//3,1//2]`
D. `[-1//3,1//2)`

Answer

C

Explanation

Let f(x)=g(x)+h(x), where
`g(x)=sqrt(1-2x) and h(x)=3 sin^(-1)((3x-1)/(2))` .
Clearly , Domain (g)`=(-oo,1//2]`
Also , h(x) is defined when
`-1 le (3x-1)/(2) le 1 implies -2 le 3x-1 le 2 implies -(1)/(3) le x le 1`
So, domain (h) `=[-1//3,1]`
Hence , domain `(f)=(-oo,1//2] cap [-1//3,1]=[-1//3,1//2]`