QJEEM24Maa04e: JEE Main 2024 Mathematics - Class 12 JEEM24Maa04e Solution: The function f ( x ) = x x 2 − 6 x − 16 , x ∈ R − { − 2 , 8 }

Question

Verified Solution • 2025–26 Session moderate

The function $f (x) = \frac{x}{x^{2} - 6 x - 16}, x \in R - {- 2, 8}$

Accepted Answer

$f (x) = \frac{x}{x^{2} - 6 x - 16}$

Now,

$\begin{aligned} f^{'} (x) = \frac{- (x^{2} + 16)}{{(x^{2} - 6 x - 16)}^{2}} \\ f^{'} (x) < 0 \end{aligned}$

Thus $f (x)$ is decreasing in

$(- \infty, - 2) \cup (- 2, 8) \cup (8, \infty)$

Step-by-Step Verified Solution