Q. If $y = 3^{x - 1} + 3^{- x - 1}(x$ real), then the least value of $y$ is
A) 2
B) 6
C) 2⁄3
D) None of these
Explanation
(c)
Given, $y = \frac{3^{x}}{3} + \frac{1}{{3.3}^{x}} = \frac{1}{3}(3^{x} + 3^{- x})$
Since, $\frac{3^{x} + 3^{- x}}{2} \geq \sqrt{3^{x}.3^{- x}\ }\ \ \ \ \lbrack\therefore AM \geq GM\rbrack$
$\Rightarrow 3^{x} + 3^{- x} \geq 2$
$\Rightarrow \ \ y \geq \frac{2}{3}$
Therefore, least value of y is $\frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.