Let f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 . Then, describe the following function: f g .

Given that: f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 We have to describe the function: f g ∵ f x = x + 1 ∴ f is defined when x + 1 ≥ 0 ⇒ x ≥ - 1 ∴ D f = - 1 , ∞ And g x = 9 - x 2 And g x is defined when 9 - x 2 ≥ 0 ⇒ x 2 - 9 ≤ 0 ⇒ x - 3 x + 3 ≤ 0 ⇒ x ∈ - 3 , 3 ∴ D g = - 3, 3 D f ∩ D g = - 1 , ∞ ∩ - 3 , 3 = - 1, 3 f g : - 1 , 3 → R Hence, f g = f x · g x = x + 1 9 - x 2 = 9 + 9 x - x 2 - x 3

Let f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 . Then, describe the following function: f g .

Given that: f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 We have to describe the function: f g We have f x = x + 1 ∴ f is defined when x + 1 ≥ 0 ⇒ x ≥ - 1 ∴ D f = - 1 , ∞ and g x = 9 - x 2 g x is defined when 9 - x 2 ≥ 0 ⇒ x 2 - 9 ≤ 0 ⇒ x - 3 x + 3 ≤ 0 ⇒ x ∈ - 3 , 3 ∴ D g = - 3, 3 D f ∩ D g = - 1 , ∞ ∩ - 3 , 3 = - 1, 3 f g : [ - 1 , 3 ) → R Hence, f g = f ( x ) g ( x ) = x + 1 9 - x 2 = x + 1 9 - x 2 .

Let f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 . Then, describe the following function: g f .

Given that: f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 We have to describe the function: g f ∵ f x = x + 1 ∴ f is defined when x + 1 ≥ 0 ⇒ x ≥ - 1 ∴ D f = - 1 , ∞ And g x = 9 - x 2 g x is defined when 9 - x 2 ≥ 0 ⇒ x 2 - 9 ≤ 0 ⇒ x - 3 x + 3 ≤ 0 ⇒ x ∈ - 3 , 3 ∴ D g = - 3, 3 D f ∩ D g = - 1 , ∞ ∩ - 3 , 3 = - 1, 3 g f : ( - 1 , 3 ] → R Hence, g f = g ( x ) f ( x ) = 9 - x 2 x + 1 = 9 - x 2 x + 1 .

Let f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 . Then, describe the following function: 2 f - 5 g .

Given that: f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 We have to describe the function: 2 f - 5 g . ∵ f x = x + 1 ∴ f is defined when x + 1 ≥ 0 ⇒ x ≥ - 1 ∴ D f = - 1 , ∞ And g x = 9 - x 2 g x is defined when 9 - x 2 ≥ 0 ⇒ x 2 - 9 ≤ 0 ⇒ x - 3 x + 3 ≤ 0 ⇒ x ∈ - 3 , 3 ∴ D g = - 3, 3 D f ∩ D g = - 1 , ∞ ∩ - 3 , 3 = - 1, 3 2 f - 5 g : - 1 , 3 → R ∴ 2 f - 5 g = 2 f x - 5 g x = 2 x + 1 - 5 9 - x 2 = 2 x + 1 - 45 - 5 x 2

Let f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 . Then, describe the following function: f 2 + 7 f .

Given that: f , g be two real functions defined by f x = x + 1 and g ( x ) = 9 - x 2 We have to the function: f 2 + 7 f ∵ f x = x + 1 ∴ f is defined when x + 1 ≥ 0 ⇒ x ≥ - 1 ∴ D f = - 1 , ∞ And g x = 9 - x 2 g x is defined when 9 - x 2 ≥ 0 ⇒ x 2 - 9 ≤ 0 ⇒ x - 3 x + 3 ≤ 0 ⇒ x ∈ - 3 , 3 ∴ D g = - 3, 3 D f ∩ D g = - 1 , ∞ ∩ - 3 , 3 = - 1, 3 f 2 + 7 f : [ - 1 , ∞ ) → R ∴ f 2 + 7 f = f 2 x + 7 f x = x + 1 2 + 7 x + 1 ⇒ f 2 + 7 f = f 2 x + 7 f x = x + 1 + 7 x + 1 Hence, f 2 + 7 f = ( x + 1 ) + 7 x + 1

If f x = log e ⁡ ( 1 - x ) and g x = x , then determine the following functions: g f . Also, find g f 1 2 .

Given f x = log e ⁡ 1 - x f ( x ) is defined only if 1 - x > 0 ⇒ x < 1 ∴ D f = - ∞ , 1 Given g x = x ∴ g is defined for all x ∈ R ∴ D g = R D f ∩ D g = - ∞ , 1 ∵ g f x = g ( x ) f ( x ) = x log e 1 - x ∴ g f 1 2 = 1 2 log e ⁡ 1 - 1 2 = 0 log e ⁡ 1 2 = 0

E M B I B E

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4

R D Sharma Solutions for Chapter: Functions, Exercise 4: EXERCISE 3.4

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Functions, Exercise 4: EXERCISE 3.4

Attempt the practice questions on Chapter 3: Functions, Exercise 4: EXERCISE 3.4 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Functions, Exercise 4: EXERCISE 3.4 with Hints & Solutions

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4>Q 4

Let $f, g$ be two real functions defined by $f (x) = \sqrt{x + 1}$ and $g (x) = \sqrt{9 - x^{2}}$ . Then, describe the following function: $f g$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4>Q 4

Let $f, g$ be two real functions defined by $f (x) = \sqrt{x + 1}$ and $g (x) = \sqrt{9 - x^{2}}$ . Then, describe the following function: $\frac{f}{g}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4>Q 4

Let $f, g$ be two real functions defined by $f (x) = \sqrt{x + 1}$ and $g (x) = \sqrt{9 - x^{2}}$ . Then, describe the following function: $\frac{g}{f}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4>Q 4

Let $f, g$ be two real functions defined by $f (x) = \sqrt{x + 1}$ and $g (x) = \sqrt{9 - x^{2}}$ . Then, describe the following function: $2 f - \sqrt{5} g$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 3 - Functions>EXERCISE 3.4>Q 4

Let $f, g$ be two real functions defined by $f (x) = \sqrt{x + 1}$ and $g (x) = \sqrt{9 - x^{2}}$ . Then, describe the following function: $f^{2} + 7 f$ .