Question

Find the domain and range of the function f(x) = sqrt(2 - x - x ^ 2) .​

Answer 1

• See below

Explanation:

Given function:

• 
  `f(x) = √(2 - x - x ^ 2)`

As any square root function, its range is all non-negative numbers:

• f(x) ≥ 0 or f(x) ∈ [0, +∞)

The domain the x values when the expression under root is non-negative:

• 2 - x - x² ≥ 0
• x² + x - 2 ≤ 0
• (x + 2)(x - 1) ≤ 0
• - 2 ≤ x ≤ 1

or

• x∈ [-2, 1]