Misc 7 - Chapter 2 Class 11 Relations and Functions

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Misc 7 Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and 𝑓/𝑔 f(x) = x + 1, g(x) = 2x – 3 (f + g) (x) = f(x) + g(x) = (x + 1) + (2x – 3) = 3x – 2 ∴(f + g) (x) = 3x – 2 (f – g) (x) = f(x) – g(x) = (x + 1) – (2x – 3) = x + 1 – 2x + 3 = – x + 4 ∴ (f – g) (x) = –x + 4 (f/g) (x) = (f(x))/(g(x)) where, g (x) ≠ 0, x ∈ R = (x + 1)/(2x − 3) Where , 2x – 3 ≠ 0 2x ≠ 0 + 3 2x ≠ 3 x ≠ 3/2 ∴(f/g) (x) = (x + 1)/(2x − 3) , where x ≠ 3/2