Find the domain of the function `f(x)=sqrt(1-2x)+3sin^(- 1)((3x-1)/2)`A. `[-1//3,1]`B. `(-oo,1//2]`C. `[-1//3,1//2]`D. `[-1//3,1//2)`

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

1.	Find the domain of the function `f(x)=sqrt(1-2x)+3sin^(- 1)((3x-1)/2)`A. `[-1//3,1]`B. `(-oo,1//2]`C. `[-1//3,1//2]`D. `[-1//3,1//2)`
Answer» Correct Answer - C 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]`

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