Question

The range of the function f(x) = x² + 2x+ 2 is ______.

Options

• (1, ∞)

• (2, ∞)

• (0, ∞)

• [1, ∞)

Answer 1

The range of the function f(x) = x² + 2x+ 2 is [1, ∞).

Explanation:

Let f(x) = y = x² + 2x + 2 = (x + 1)² + 1

y – 1 = (x + 1)²

`\implies` x + 1 = `sqrt(y - 1)`

x = `sqrt(y - 1) - 1`

Since, y – 1 ≥ 0

∴ y ≥ 1

∴ Range is [1, ∞).