Let f : R → R : f ( x ) = x 3 + 1 . Find 1 f x

Given f ( x ) = x 3 + 1 Now, 1 f ( x ) = 1 f ( x ) = 1 x 3 + 1 Therefore 1 f ( x ) = 1 x 3 + 1

Let f : R → R : f ( x ) = x 3 + 1 and g : R → R : g ( x ) = ( x + 1 ) . Find f g x

Given f ( x ) = x 3 + 1 and g ( x ) = x + 1 Now, f g ( x ) = f ( x ) g ( x ) = x 3 + 1 x + 1 = ( x + 1 ) x 2 - x + 1 x + 1 ∵ a 3 + b 3 = ( a + b ) a 2 - a b + b 2 Therefore f g ( x ) = x 2 - x + 1

Let f : R → R ; f x = x c , where c is a constant. Find ( c f ) ( x )

Given f ( x ) = x c We know that ( c f ) ( x ) = c · f ( x ) = c · x c = x Therefore, ( c f ) ( x ) = x

Let f : R → R ; f x = x c where c is a constant. Find c 2 f ( x )

Given f ( x ) = x c We know that c 2 f ( x ) = c 2 · f ( x ) = c 2 · × x c = c x Therefore c 2 f ( x ) = c x

Let f : R → R ; f x = x c where c is a constant. Find 1 c f ( x )

Given f ( x ) = x c We know that 1 c f x = 1 c · f ( x ) = 1 c x c = x c 2 Therefore. 1 c f ( x ) = x c 2

Let f : ( 2 , ∞ ) → R : f ( x ) = x - 2 and g : ( 2 , ∞ ) → R : g ( x ) = x + 2 . Find f + g x .

Given: f ( x ) = x - 2 : x > 2 and g ( x ) = x + 2 ; x > 2 Domain ( f ) = ( 2 , ∞ ) Range ( f ) = ( 0 , ∞ ) Domain ( g ) = ( 2 , ∞ ) Range ( g ) = ( 2 , ∞ ) We know that ( f + g ) ( x ) = f ( x ) + g ( x ) = x - 2 + x + 2 Therefore, ( f + g ) ( x ) = x - 2 + x + 2

Let f : ( 2 , ∞ ) → R : f ( x ) = x - 2 and g : ( 2 , ∞ ) → R : g ( x ) = x + 2 . Find ( f - g ) ( x )

Given: f ( x ) = x - 2 : x > 2 and g ( x ) = x + 2 Range ( g ) ⊆ Domain ( f ) Therefore, ( f - g ) ( x ) exists. We know that ( f - g ) ( x ) = f ( x ) - g ( x ) = x - 2 - x + 2 Therefore, ( f - g ) ( x ) = x - 2 - x + 2

Let f : ( 2 , ∞ ) → R : f ( x ) = x - 2 and g : ( 2 , ∞ ) → R : g ( x ) = x + 2 . Find ( f g ) ( x )

Given: f ( x ) = x - 2 : x > 2 and g ( x ) = x + 2 We know that ( f g ) ( x ) = f ( x ) · g ( x ) = ( x - 2 ) ( x + 2 ) = x 2 - 2 2 ∵ a 2 - b 2 = ( a - b ) ( a + b ) = x 2 - 4 Therefore, ( f g ) ( x ) = x 2 - 4

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Set and Functions>Chapter 3 - Functions>EXERCISE 3E

R S Aggarwal Solutions for Exercise 5: EXERCISE 3E

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 5: EXERCISE 3E

Attempt the practice questions from Exercise 5: EXERCISE 3E with hints and solutions to strengthen your understanding. Senior Secondary School Mathematics FOR CLASS 11 solutions are prepared by Experienced Embibe Experts.