Question

If a function \( f : [2, \infty) \to \mathbb{R \) is defined by} \[ f(x) = x^2 - 4x + 5 \] then the range of \( f \) is:

• A. \( [2, \infty) \)
• B. \( [5, \infty) \)
• C. \( \mathbb{R} \)
• D. \( [1, \infty) \)

Hint:

For a quadratic function \( f(x) = ax^2 + bx + c \), the vertex occurs at \( x = \frac{-b}{2a} \), and the range depends on whether the parabola opens upwards (if \( a > 0 \)) or downwards (if \( a < 0 \)).

Answer 1

The Correct Option is D