# 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 - Mathematics

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 Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.4 | Q 1.2 | Page 38