First slide

Functions (XII)

Question

$Range of the expression f (x) = \frac{x^{3} + x^{2} + x - 3}{x - 1} is$

Moderate

A

$[2, \infty)$
B

$(2, \infty)$
C

$[2, \infty) - {6}$
D

$(- 1, \infty)$

Solution

$f (x) = \frac{x^{3} + x^{2} + x - 3}{x - 1}, x \neq 1$
$= \frac{(x^{2} + 2 x + 3) (x - 1)}{x - 1}, x \neq 1$
$= x^{2} + 2 x + 3, x \neq 1$
$= {(x + 1)}^{2} + 2 \geq 2, x \neq 1$
Range of the given function = [2, $\infty$ )

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