(x^2 5x+7)(x^2 x)(x+1)≥ 0 Term: x^2 5x+7, D lt;0, a gt;0 ⇒ gt;0 ∀ x∈ R ⇒x(x 1)(x+1)≥ 0 Range is x∈ ( ∞, 1)∪[0,1] ...

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Using Monotonicity to Find the Range of a Function

x2-5x+7x2-xx+...

Question

$\frac{(x^{2} - 5 x + 7) (x^{2} - x)}{(x + 1)} \geq 0$

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Solution

$\frac{(x^{2} - 5 x + 7) (x^{2} - x)}{(x + 1)} \geq 0$
Term: $x^{2} - 5 x + 7, D < 0, a > 0 \Rightarrow> 0 \forall x \in R$
$\Rightarrow \frac{x (x - 1)}{(x + 1)} \geq 0$

Range is $x \in (- \infty, - 1) \cup [0, 1]$

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