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

  1. Chapter 2 Class 11 Relations and Functions
  2. Serial order wise
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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) = โˆšx + x, (f โ€“ g) (x) = f(x) โ€“ g(x) = โˆšx 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‘ฅ^(3/2) (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 (f/g) (x) = 1/โˆš๐‘ฅ where x โ‰  0

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