Last updated at Jan. 28, 2020 by Teachoo
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Example 16 Let f(x) = x2and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f โ g) (x), (fg) (x), ("f" /๐) (x) f(x) = x2 & g(x) = 2x + 1 (f + g) (x) = f(x) + g(x) = (x2) + (2x + 1) = x2 + 2x + 1, โด(f + g) (x) = x2 + 2x + 1 (f โ g) (x) = f(x) โ g(x) = (x2) โ (2x + 1) = x2 โ 2x โ 1 โด (f โ g) (x) = x2 โ 2x โ 1 f(x) = x2 & g(x) = 2x + 1 (fg) (x) = f(x) ร g(x) = x2 (2x + 1) = x2 (2x) + x2 (1) = 2x3 + x2, โด (fg) (x) = 2x3 + x2, (f/g) (x) = (f(x))/(g(x)) where, g (x) โ 0, x โ R = x2/(2x + 1) Example 16 Let f(x) = x2and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f โ g) (x), (fg) (x), ("f" /๐) (x) f(x) = x2 & g(x) = 2x + 1 (f + g) (x) = f(x) + g(x) = (x2) + (2x + 1) = x2 + 2x + 1, โด(f + g) (x) = x2 + 2x + 1 (f โ g) (x) = f(x) โ g(x) = (x2) โ (2x + 1) = x2 โ 2x โ 1 โด (f โ g) (x) = x2 โ 2x โ 1 f(x) = x2 & g(x) = 2x + 1 (fg) (x) = f(x) ร g(x) = x2 (2x + 1) = x2 (2x) + x2 (1) = 2x3 + x2, โด (fg) (x) = 2x3 + x2, (f/g) (x) = (f(x))/(g(x)) where, g (x) โ 0, x โ R = x2/(2x + 1) Where , 2x + 1 โ 0 2x โ 0 โ 1 2x โ โ 1 x โ (โ1)/2 โด (๐/๐ ) (x) = ๐๐/(๐๐ + ๐) , where x โ (โ๐)/๐
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