Algebra of functions: 

Consider two functions be f: D_1→ R and g: D₂ → R. We define functions f + g, f - g, f. g and f /g as follows:

•   f + g : D  → R is a function shown by

            (f + g)x = f(x) + g(x)               where D = D₁∩ D₂

•   f  - g : D → R is a function shown by

            (f - g)x = f(x) -g(x)                 where D = D₁∩D₂

•   f . g  :   D → R is  a function shown by

            by (f . g)x = f(x). g(x)             where D = D₁∩ D₂

•   f / g  :     D → R is  a function shown by

            (f /g)x = ƒ(x)/g(x)                   where D = D₁∩{x∈D₂: g(x) ≠ 0}

Problem: Suppose f(x) = sin^-1x,  g(x) =. calculate f + g, f - g, f . g and f /g

Solution:            

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