Check sibling questions

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

Example 16 - Chapter 2 Class 11 Relations and Functions - Part 2
Example 16 - Chapter 2 Class 11 Relations and Functions - Part 3


Transcript

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 f(x) = x2 & g(x) = 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) 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 f(x) = x2 & g(x) = 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) = π’™πŸ/(πŸπ’™ + 𝟏) , where x β‰  (βˆ’πŸ)/𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.