Find the range of
(a) `f(x) = x^(2) + 2x + 4`
(b) `f(x) = 1+x -x^(2)`

Explanation

(a) `f(x) = x^(2) + 2x + 4 = (x + 1)^(2) + 3`
As `(x+1)^(2) ge 0, x in R`
`rArr f(x) ge 3 rArr "Range" = [3, oo)`
(b) `f(x) = 1 + x - x^(2) = 1- (x^(2) - x + (1)/(4) - (1)/(4)) = 1-(x-(1)/(2))^(2) + (1)/(4)`
`= (5)/(4) - (x - (1)/(2))^(2)`
As `(x-(1)/(2))^(2) ge 0 rArr f(x) le (5)/(4)`
`rArr` Range `= (-oo, (5)/(4)]`