Let `f:R to R ` be the function defined by ` f(x) = (1)/(2-cos x), AA x in R.` Then, find the range fo `f`.

Answer

N/a

Explanation

Given function, `f(x)=(1)/(2-"cos"x), AA x in R`
Let ` y=(1)/(2-"cos" x)`
`implies 2y-y cos x=1`
`implies y cos x= 2y-1`
`impliescos x=(2y-1)/(y)=2 - (1)/(y) impliescos x = 2-(1)/(y)`
`implies -1 le cos x le 1 implies -1 le 2 - (1)/(y) le 1`
` implies -3 le -(1)/(y) le -1 implies 1 le (1)/(y) le 3`
`implies (1)/(3) le (1)/(y) le 1`
So, y range is `[(1)/(3),1]`.