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Find F + G, F − G, Cf (C ∈ R, C ≠ 0), Fg, 1 F and F G in : (B) If F ( X ) = √ X − 1 and G ( X ) = √ X + 1 - CBSE (Science) Class 11 - Mathematics

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Question

Find f + gf − gcf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{  and } \frac{f}{g}\] in : 

(b) If \[f\left( x \right) = \sqrt{x - 1}\]  and  \[g\left( x \right) = \sqrt{x + 1}\]

 

Solution

Given: \[f\left( x \right) = \sqrt{x - 1}\] and \[g\left( x \right) = \sqrt{x + 1}\] Thus,
(g) ) : [1, ∞) → R is defined by (f + g) (x) = (x) + g (x) = \[\sqrt{x - 1} + \sqrt{x + 1}\] (f -  g) ) : [1, ∞) → R is defined by (f - g) (x) = (x) -  g (x) = \[\sqrt{x - 1} - \sqrt{x + 1}\] cf : [1, ∞) → R is defined by (cf) (x) = \[c\sqrt{x - 1}\] (fg) : [1, ∞) → R is defined by (fg) (x) = f(x).g(x) = (fg) :

[1, ∞) → R is defined by (fg) (x) = f(x).g(x) = \[\sqrt{x - 1} \times \sqrt{x + 1} = \sqrt{x^2 - 1}\]

\[\frac{1}{f}: \left( 1, \infty \right) \to \text{ R isdefined by } \left( \frac{1}{f} \right)\left( x \right) = \frac{1}{f\left( x \right)} = \frac{1}{\sqrt{x - 1}} . \] \[\frac{f}{g}: [1, \infty ) \to \text{ R is defined by } \left( \frac{f}{g} \right)\left( x \right) = \frac{f\left( x \right)}{g\left( x \right)} = \frac{\sqrt{x - 1}}{\sqrt{x + 1}} = \sqrt{\frac{x - 1}{x + 1}} .\]

 
 
 
 

 

 
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APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 3: Functions
Ex.3.40 | Q: 1.2 | Page no. 38
Solution Find F + G, F − G, Cf (C ∈ R, C ≠ 0), Fg, 1 F and F G in : (B) If F ( X ) = √ X − 1 and G ( X ) = √ X + 1 Concept: Cartesian Product of Sets.
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