We propose the abstractions of Functional Encryption (FE) and Indistinguishability Obfuscation (iO) for pseudorandom functionalities which are strictly weaker than their general counterparts. Intuitively, a pseudorandom functionality means that the output of the circuit is indistinguishable from uniform for every input seen by the adversary. We then leverage weak indistinguishability style security of these tools to obtain the following applications: We provide heuristic constructions of FE and MIFE for pseudorandom functionalities from private coin evasive LWE and plain LWE, where private coin evasive LWE is suitably parametrized to avoid all know attacks for the functionalities we consider in this work. This implies iO for pseudorandom functionalities from the same assumptions.