Question

The range of f(x)= x² + x +1​

Answer 1

Answer:

For such questions, first complete the squares. The answer would be simpler than you think.

y=x2−x−1=(x−1/2)2−1/4−1=(x−1/2)2−54

ymin=−5/4 when x=1/2

ymax→∞ when x→∞

Range =[−5/4,∞)

Answer 2

The range of the function f(x) = x² + x + 1 is [1,∞).

Closed bracket → [ and ]

Open bracket → ( and )

This function can give output of any real number ranging from 1 to ∞.