Question

If $y=3^{x-1}+3^{-x-1}$ (x real), then the least value of y is

• A. 2
• B. 6
• C. $\frac{2}{3}$
• D. None of these

Answer 1

The correct option is C $\frac{2}{3}$

We have
$3^{x-1}+3^{-x-1}=\frac{1}{3}(3^x+3^{-x})\ge \frac{1}{3}.2\sqrt{3^x.3^{-x}}$,
$[\because A.M.\ge G.M.]$
or $3^{x-1}+3^{-x-1}\ge \frac{2}{3}$
Hence the least value of $3^{x-1}+3^{-x-1}$ is $\frac{2}{3}$