Question

sendo f(x) = a^x + a^-x
tudo sobre(dividido por) 2


calcule f(1) + f(-1)

Answer 1

f(x)=[(a^x)+(a^-x])/2

Para x=1
f(x)=[(a^x)+(a^-x])/2
f(1)=[(a^1)+(a^-1])/2
f(1)=[a+1/a]/2

Para x=-1
f(x)=[(a^x)+(a^-x])/2
f(-1)={[a^-1]+[a^-(-1)]}/2
f(-1)={[1/a+a^1]}/2
f(-1)=[1/a+a]/2

f(1)+f(-1)
[a+1/a]/2+[1/a+a]/2
2[a+1/a]/2
a+1/a