Question

the functional relationship between inputs and outputs in the production

Answer 1

The production function specifies either the maximum output that can be produced with the given inputs or the minimum quantity of inputs needed to produce a given level of output. ... Production function establishes a relation between inputs and output, which is technical in nature.

Answer 2

The functional relation between output and input is input provide raw materials to specific industry so that it provide output to the people .  Without input we can't produce output.