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Example 17 - Let f(x) = root x, g(x) = x. Find f + g, fg, f/g

Example 17 - Chapter 2 Class 11 Relations and Functions - Part 2

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Example 17 Let f(x) = โˆš๐‘ฅ 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) = โˆš๐ฑ + x, (f โ€“ g) (x) = f(x) โ€“ g(x) = โˆš๐ฑ โ€“ x (fg) x = f(x) ร— g(x) = โˆšx ร— x = ๐‘ฅ^(1/2) ร— x1 = ๐‘ฅ^(1/2+1) = ๐‘ฅ^((1+2)/2) = ๐’™^(๐Ÿ‘/๐Ÿ) (f/g) (x) = (f(x))/(g(x)) where, g (x) โ‰  0, x โˆˆ R = โˆš๐‘ฅ/(x ) = โˆš๐‘ฅ/(โˆš๐‘ฅ ร—โˆš๐‘ฅ) = 1/โˆš๐‘ฅ Where , โˆš๐‘ฅ โ‰  0 โ‡’ x โ‰  0 โˆด (๐Ÿ/๐ ) (x) = ๐Ÿ/โˆš๐’™ where x โ‰  0

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.