Explanation

(c)
Given, inequality can be rewritten as $\left( \frac{5}{13} \right)^{x} + \left( \frac{12}{13} \right)^{x} \geq 1$
$\therefore\cos^{x}{\alpha + {\sin^{x}\alpha}{\geq 1}}$
Where, $\cos{\alpha = \frac{5}{13}}$
If $x = 2,$ the above equality holds
If $x < 2$ both $\cos\alpha\$and $\sin\alpha\$increases in positive fraction
Hence, above inequality holds for $x \in ( - \infty,2\rbrack$