Prove that $ f(x|\theta) = \frac{1}{4} e^{-\frac{1}{2}|x-\theta|}$ is not an exponential family.

Question

I want to prove that $ f(x|\theta) = \frac{1}{4} e^{-\frac{1}{2}|x-\theta|}$ does not belong to the exponential family.

By definition, it is easy to answer such questions as 'prove a given distribution fuction is in the exponential family', but I fail to copy with this question to prove "does not belong to the exponential family". Any idea? Thanks.