Explain Algebraic Operations on Functions ?

1.	Explain Algebraic Operations on Functions ?
Answer» If f and g are real valued functions of x with domain set A and B respectively, then both f and g are defined in A ∩ B. Then, (a) (f + g) x = f (x) + g(x) : Domain A ∩ B (b) (f – g) x = f (x) – g(x) : Domain A ∩ B (c) (fg) x = f (x) . g(x) : Domain A ∩ B (d) \(\big[\frac{f}{g}\big]x = \frac{f(x)}{g(x)}\) : Domain A ∩ B (e) (f + k) x = f (x) + k : k is constant, so domain = A (f) (kf ) x = k f (x) (g) f ⁿ(x) = [f (x)]ⁿ

Answer»

If f and g are real valued functions of x with domain set A and B respectively, then both f and g are defined in A ∩ B. Then,

(a) (f + g) x = f (x) + g(x) : Domain A ∩ B

(b) (f – g) x = f (x) – g(x) : Domain A ∩ B

(d) \(\big[\frac{f}{g}\big]x = \frac{f(x)}{g(x)}\) : Domain A ∩ B

(e) (f + k) x = f (x) + k : k is constant, so domain = A

(f) (kf ) x = k f (x)

(g) f ⁿ(x) = [f (x)]ⁿ

Discussion