1)

f(x)=a^(x- 1)

f(2)=a^(2- 1)= 1/2

a= 1/2

2)

F (x) = (1/2) (x- 1) is a monotonically decreasing function.

3)

g(x)=a^(x^2+2x)=( 1/2)^(x^2+2x)=( 1/2)^[(x+ 1)^2- 1]<； =( 1/2)^(- 1)=2

Because: g(x)>0

So: the range is (0,2)