The function `f: RvecR` is defined by `f(x)=cos^2x+sin^4xdotT h e n ,f(R)=` `[3//4,1)` (b) `(3//4,1]` (c) `[3//4,1]` (d) (`3//4,1)`

Explanation

Given:
`f(x)=cos^2x+sin^4x`
`f(x)=cos^2x+sin^2x times sin^2x`
`f(x)=cos^2x+sin^2x(1-cos^2x)`
`f(x)=cos^2x+sin^2x-sin^2xcos^2x`
Using Identity
`cos^2x+sin^2x=1`
`f(x)=1-sin^2xcos^2x`
`f(x)=1-1/4sin^22x`
`3/4 le f(x) le 1`
`f(x) in [3/4,1]`