Question

Find the range of `f(x)=sin^2x-sinx+1.`

Answer 1

`f(x)=sin^(2)x-sinx +1=(sinx - (1)/(2))^(2)+(3)/(4)`
Now, ` -1 le sinx le 1 " or " -(3)/(2) le sinx-(1)/(2) le (1)/(2)`
or ` o le (sinx -(1)/(2))^(2) le (9)/(4) " or " (3)/(4) le (sinx -(1)/(2))^(2) l+ (3)/(4) le 3`
Hence, the range is `[(3)/(4),3]`.