That is, the maximum value of the function f (x) = a x is less than 2.

Y = a x is a monotone function, and the maximum value is obtained at the endpoint.

∴a^2<； 2 and a (-2) < 2

∴a & lt； √2 and a & gt√2/2

To sum up, the range of a is (√2/2, 1)U( 1, √2).