JEE PYQ: Sequence And Series Question 39
Question 39 - 2020 (08 Jan Shift 1)
Let $f : R \to R$ be such that for all $x \in R$, $(2^{1+x} + 2^{1-x})$, $f(x)$ and $(3^x + 3^{-x})$ are in A.P., then the minimum value of $f(x)$ is:
(1) 2
(2) 3
(3) 0
(4) 4
Show Answer
Answer: (2)
Solution
If $2^{1-x} + 2^{1+x}$, $f(x)$, $3^x + 3^{-x}$ are in A.P., then
$f(x) = \frac{2^{1+x} + 2^{1-x} + 3^x + 3^{-x}}{2}$
$2f(x) = 2\left(2^x + \frac{1}{2^x}\right) + \left(3^x + \frac{1}{3^x}\right)$
Using AM $\geq$ GM
$f(x) \geq 3$
BETA
