Find the domain and the range of the real function: f ( x ) = a x - b c x - d

Given, f x = a x - b c x - d We know that function is not defined if denominator is zero ∴ f ( x ) will be defined if c x - d ≠ 0 ⇒ x ≠ d c Therefore, the domain of function is D f = R - d c . Let f x = y = a x - b c x - d ⇒ c x y - d y = a x - b ⇒ c x y - a x = d y - b ⇒ x = d y - b c y - a Now, x will not be defined when c y - a = 0 ⇒ y = a c Therefore, the range of function is R f = R - a c .

Find the domain and the range of the real function f ( x ) = x 2 - 9 x - 3

Given f ( x ) = x 2 - 9 x - 3 For D f ; f ( x ) must be a real number ⇒ x 2 - 9 x - 3 must be a real number. ⇒ x - 3 ≠ 0 ⇒ x ≠ 3 ∴ D f = R - { 3 } For R f ; Let y = f ( x ) = x 2 - 9 x - 3 , x ≠ 3 ⇒ y = ( x - 3 ) ( x + 3 ) x - 3 = x + 3 ( ∵ x ≠ 3 ) ⇒ x = y - 3 since x ≠ 3 ⇒ y ≠ 6 , also x ∈ R ⇒ x + 3 ∈ R ⇒ y ∈ R ∴ R f = R - { 6 }

E M B I B E

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

R S Aggarwal Solutions for Exercise 3: EXERCISE 3C

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 3: EXERCISE 3C

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