Last updated at Jan. 28, 2020 by Teachoo
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Example 17 Let f(x) = โ๐ฅ and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (f + g) (x), (f โ g) (x), (fg) (x) and (๐/๐) (x) (f + g) (x) = f(x) + g(x) = โ๐ฑ + x, (f โ g) (x) = f(x) โ g(x) = โ๐ฑ โ x (fg) x = f(x) ร g(x) = โx ร x = ๐ฅ^(1/2) ร x1 = ๐ฅ^(1/2+1) = ๐ฅ^((1+2)/2) = ๐^(๐/๐) (f/g) (x) = (f(x))/(g(x)) where, g (x) โ 0, x โ R = โ๐ฅ/(x ) = โ๐ฅ/(โ๐ฅ รโ๐ฅ) = 1/โ๐ฅ Where , โ๐ฅ โ 0 โ x โ 0 โด (๐/๐ ) (x) = ๐/โ๐ where x โ 0
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