Example 16 - Chapter 2 Class 11 Relations and Functions
Last updated at April 16, 2024 by Teachoo
Examples
Example 1
Example 2
Example 3 Important
Example 4 Important
Example 5
Example 6 Important
Example 7
Example 8 Important
Example 9 Important
Example 10
Example 11 (i)
Example 11 (ii) Important
Example 11 (iii) Important
Example 12
Example 13
Example 14 Important
Example 15 Important
Example 16 You are here
Example 17 Important
Example 18
Example 19
Example 20 Important
Example 21 Important
Example 22 Important
Chapter 2 Class 11 Relations and Functions
Serial order wise
- Ex 2.1
- Ex 2.2
- Ex 2.3
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Examples
- Miscellaneous
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) × 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) ≠ 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) × 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) ≠ 0, x ∈ R = x2/(2x + 1) Where , 2x + 1 ≠ 0 2x ≠ 0 – 1 2x ≠ – 1 x ≠ (−1)/2 ∴ (𝐟/𝐠) (x) = 𝒙𝟐/(𝟐𝒙 + 𝟏) , where x ≠ (−𝟏)/𝟐
