Question

show that a^x + a^(-x) is an even function ?

Answer 1

As we know ,
Functions are even or odd..

Here The L' Hospital rule can't be applied

$\implies$ F(x) =a^x a^-x

$\implies$ Then f(x)=
${a}^{ - x} + {a}^{ - ( - x)} \\ \\ = {a }^{ - x} + {a}^{x} \\ \\ = f(x)$

$\implies$ Hence f(x) is an Even function.

Answer 2

Heya _____

Que ____ show that a^x + a^(-x) is an even function ____

Answer is as given ______

f(x) = a^x + a^(-x)

a^-x + a-(-x)

a^-x + a^x

f(x)


So... it is an even function...

Thank you