Question

Four functions are defined on set R_o, Such that,
f₁(x) = x, f₂(x) = -x, f₃(x) = 1/x, f₄(x) = – 1/x Construct the composition table for the composition of functions f₁, f₂, f₃, f₄. Also, find identity element and inverse of every element.

Answer 1

Given,

f₁(x) = x, f₂(x) = – x,

∴ Table for above operations

Hence, it is clear that f₁ is identity function of f₁, f₂, f₃, f₄.

Hence, inverse element is itself too.