First slide

Means - A.M/G.M/H.M

Question

$\begin{array}{l} Let f : R \to R be such that for all x \in R, (2^{1 + x} + 2^{1 - x}), f (x) and (3^{x} + 3^{- x}) are in A.P. Then the \\ minimum value of f (x) is: \end{array}$

Moderate

A

2
B

3
C

4
D

0

Solution

$\begin{array}{l} f (x) = (\frac{2^{1 - x} + 2^{1 + x} + 3^{x} + 3^{- x}}{2}) = (2^{x} + \frac{1}{2^{x}}) + \frac{1}{2} (3^{x} + \frac{1}{3^{x}}) \geq 2 + 1 \\ \Rightarrow f (x) \geq 3 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App