Fully homomorphic encryption (FHE), which is used to evaluate arbitrary functions in addition and multiplication operations via modular arithmetic (mod q) over ciphertext, can be applied in various privacy-preserving applications. However, big data is difficult to adopt owing to its high computational cost and the challenges associated with the efficient handling of complex functions such as log(x). To address these problems, we propose a method for handling any multi-input function using a lookup table (LUT) to replace the original calculations with array indexing operations over integer-based FHE. In this study, we extend our LUT-based method to handle any input values, i.e., including non-matched element values in the LUT, to match with a near indexed value and return an approximated output over FHE. In addition, we propose a technique for splitting the table to handle large integers for improved accuracy with only a slight increase in the execution time. For the experiments, we use the Microsoft/SEAL library, and the results show that our proposed method can evaluate a 16-bit to 16-bit function in 2.110 s and a 16-bit to 32-bit function in 2.268 s, thereby outperforming previous methods implemented via bit-wise calculation over FHE.