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Last updated at Jan. 28, 2020 by Teachoo
Example 17 Let f(x) = βπ₯ and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (f + g) (x), (f β g) (x), (fg) (x) and (π/π) (x) (f + g) (x) = f(x) + g(x) = βπ± + x, (f β g) (x) = f(x) β g(x) = βπ± β x (fg) x = f(x) Γ g(x) = βx Γ x = π₯^(1/2) Γ x1 = π₯^(1/2+1) = π₯^((1+2)/2) = π^(π/π) (f/g) (x) = (f(x))/(g(x)) where, g (x) β 0, x β R = βπ₯/(x ) = βπ₯/(βπ₯ Γβπ₯) = 1/βπ₯ Where , βπ₯ β 0 β x β 0 β΄ (π/π ) (x) = π/βπ where x β 0