The number of solutions (real) of the equation $cos (e^{x}) = 7^{x} + 7^{- x}$ is

0

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1

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Infinite

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Solution

The correct option is A $0$
$\frac{7^{x} + 7^{- x}}{2} \geq 1$ $(u s i n g A M \geq G M) \Rightarrow 7^{x} + 7^{- x} \geq 2 \Rightarrow cos (e^{x}) \geq 2$ \
which is not possible (as $- 1 \leq cos t \leq 1) ∴$
The given equation has no solution.

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