(1)
f(2)=(1/2)[a²+(1/a)²]=41/9
a²+(1/a²)=41/9
9a⁴-82a²+9=0
(9a²-1)(a²-9)=0
a=1/3或a=3
f(x)=(1/2)[3^x+(1/3)^x]
(2)
f'(x)=(1/2)[3^x-3^(-x)]
当x>0时
f'(x)>0
f(x)在[0,+∞)单调递增
(1)
f(2)=(1/2)[a²+(1/a)²]=41/9
a²+(1/a²)=41/9
9a⁴-82a²+9=0
(9a²-1)(a²-9)=0
a=1/3或a=3
f(x)=(1/2)[3^x+(1/3)^x]
(2)
f'(x)=(1/2)[3^x-3^(-x)]
当x>0时
f'(x)>0
f(x)在[0,+∞)单调递增