Question

The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______

Options

• R -`[1/2, 1]`

• R

• R - {0}

• R - {1, 2}

Answer 1

The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is R - {0},

Explanation:

f(x) is defined for x³ - 4x² + 5x - 2 ≠ 0, i.e., x ≠ 1, 2

∴ Dom(f) = R - {1, 2}

Let y = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2) = 1/(x - 1)`

⇒ x = `(1 + y)/y`

x is real for y ≠ 0

Hence, range(f) = R - {0}