यदि `f:R rarr R` एक फलन हो, तो `f^(-1):R rarr R` प्राप्त होगा यदि `f` हो

Explanation

`f(x) = sin^(2)x + sin^(2)(x+pi//3) + cos x cos (x+pi//3)`
`= (1)/(2)[2 sin^(2) x + 2sin^(2)(x+(pi)/(3))+2 cos x cos (x+(pi)/(3))]`
`= (1)/(2)[1-cos 2x + 1- cos(2x+(2pi)/(3)) + cos(2x+(pi)/(3))+cos.(pi)/(3)]`
`= (1)/(2)[(5)/(2) - cos 2x-cos (2x+(2pi)/(3))+cos (2x+(2pi)/(3))]`
`=(1)/(2)[(5)/(2)-{cos(2x)+cos(2x+(2pi)/(3))}+cos(2x+(pi)/(3))]`
`=(1)/(2)[(5)/(2)-2 cos(2x-(pi)/(3))cos.(pi)/(3)+cos(2x+(pi)/(3))]`
`=(1)/(2)[(5)/(2)-cos(2x+(pi)/(3))+cos(2x+(pi)/(3))]`
`=(5)/(4)`, सभी `x in R`
इसलिए, प्रत्येक `x in R` के लिए
`(gof)(x) = g(f(x)) = g((5)/(4)) = 1`
इस प्रकार, `(gof)(x) = 1` सभी `x in R`
अतः `(gof) : R rarr R` एक अचर फलन है।