( 1)x & lt； 1/a，g '(x)& lt； 0, g(x) is a decreasing function and f(x) is a decreasing function.

(2)x & gt； 1/a, g'(x) is increasing function, and f(x) is increasing function.

When x= 1/a, f( 1/a) takes the minimum value.

Given f (x) >: F( 1)=0 is the minimum value when x = 1, so a= 1.