Statement 1: The range of `f(x)=sin^(2)x-sinx+1` is `[3/4,oo)`.
Statemen 2: The range of `f(x)=x^(2)-x+1` is `[3/4,oo)AAxepsilonR`.

Options

A. Statement 1 is True, Statement 2 is True, Statement -2 is a correct explanation for Statement -1
B. Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statemnt -1
C. Statement -1 is True, Statement -2 is False
D. Statement -1 is False, Statement -2 is True

Answer

D

Explanation

Statement 1: `f(x)=sin^(2)x-sinx+1`
`=(sinx-1/2)^(2)+3/4`
`f(x)` is min at `sin x=1/2impliesf_(min)=3/4`
`f(x)` is max when `sinx=-1impliesf_(max)=3`
`:.` range is `[3/4,3]`
hence Statement-1 is wrong. Statement -2 is correct.