no spidey ur answer is wrong see

f(x) = 1/(2-3Sinx)

when sinx tends to 2/3 from left(i.e just less than 2/3)

f(x) tends to +ve infinity

 

when sinx tends to 2/3 from right (i.e just greater than 2/3)

f(x) tends to -ve infinity

also using boundary condition for sinx when sinx = 1 f(x) = -1 and when sinx = -1 f(x) = 1/5

so it's clear that f(x) can't lie between (-1,1/5)