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Example 16 - Let f(x) = x2 and g(x) = 2x + 1. Find f + g, fg,f/g - Algebra of real functions

  1. Chapter 2 Class 11 Relations and Functions
  2. Serial order wise
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Example 16, Let f(x) = x2and g(x) = 2x + 1 be two real functions.Find (f + g) (x), (f – g) (x), (fg) (x), ("f" /𝑔) (x) f(x) = x2 & g(x) = 2x + 1 (f + g) (x) = f(x) + g(x) = (x2) + (2x + 1) = x2 + 2x + 1, ∴(f + g) (x) = x2 + 2x + 1 (f – g) (x) = f(x) – g(x) = (x2) – (2x + 1) = x2 – 2x – 1 ∴ (f – g) (x) = x2 – 2x – 1 (fg) (x) = f(x) Γ— g(x) = x2 (2x + 1) = x2 (2x) + x2 (1) = 2x3 + x2, ∴ (fg) (x) = 2x3 + x2, (f/g) (x) = (f(x))/(g(x)) where, g (x) β‰  0, x ∈ R = x2/(2x + 1) Where , 2x + 1 β‰  0 2x β‰  0 – 1 2x β‰  – 1 x β‰  (βˆ’1)/2 ∴ (f/g) (x) = x2/(2x + 1) , where x β‰  (βˆ’1)/2

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