Question

The domain of the function
$f\left(x\right)=\sqrt{2x^3−5x^2−4x+10}$ is

• A. $\left[−\sqrt{2},\sqrt{2}\right]∪[\frac{1}{2},∞)$
• B. $\left[−\sqrt{3},\sqrt{3}\right]∪[\frac{5}{2},∞)$
• C. $\left[−\sqrt{2},\sqrt{2}\right]∪[\frac{5}{2},∞)$
• D. $\left[−\sqrt{2},\sqrt{2}\right]∪[\frac{5}{2},10)$

Answer 1

Answer: (C)

We have, $f(x)=\sqrt{2x^3−5x^2−4x+10}$
$f(x)$ is defined if $2x^3−5x^2−4x+10â‰\yen 0$
$⇒x^2(2x−5)−2(2x−5)â‰\yen 0$
$⇒(2x−5)(x^2−2)â‰\yen 0$
$⇒xâ‰\yen \frac{5}{2}$ or $−\sqrt{2}≤x≤\sqrt{2}$
$∴D_f=[−\sqrt{2},\sqrt{2}]∪[\frac{5}{2},∞)$