Consider the function f : 0 , π 2 → ℝ given by f ( x ) = sin ⁡ x and g : 0 , π 2 → ℝ given by g x = cos x . Show that f and g are one-one functions.

Given that the function f : 0 , π 2 → ℝ given by f ( x ) = sin ⁡ x and g : 0 , π 2 → ℝ given by g x = cos x . One-One function states that every element of the function's codomain is the image of at most one element of its domain. Consider f x = sin x Now, f x 1 = f x 2 ⇒ sin x 1 = sin x 2 ⇒ x 1 = x 2 Consider g x = cos x Now, g x 1 = g x 2 ⇒ cos x 1 = cos x 2 ⇒ x 1 = x 2 Therefore, f and g are one-one functions.

Consider the function f : 0 , π 2 → ℝ given by f ( x ) = sin ⁡ x and g : 0 , π 2 → ℝ given by g x = cos x . Is f + g is one-one?why?

Given that the function f : 0 , π 2 → ℝ given by f ( x ) = sin ⁡ x and g : 0 , π 2 → ℝ given by g x = cos x . One-One function states that every element of the function's codomain is the image of at most one element of its domain. We know that f + g x = f x + g x ⇒ f + g x = sin x + cos x Now, f + g 0 = sin 0 + cos 0 = 0 + 1 = 1 f + g π 2 = sin π 2 + cos π 2 = 1 + 0 = 1 Since different elements 0 , π 2 have same image 1 Therefore, f + g is not a one-one function.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Relations and Functions>Kerala Board-2019

Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Kerala Board-2019

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Kerala Board-2019

Attempt the free practice questions on Chapter 1: Relations and Functions, Exercise 1: Kerala Board-2019 with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Kerala Board-2019 with Hints & Solutions

EASY

12th Kerala Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Relations and Functions>Kerala Board-2019>Q 7

The function $P$ is defined as “To each person on the earth is assigned a date of birth”. Is this function one-one ? Given reason.

EASY

12th Kerala Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Relations and Functions>Kerala Board-2019>Q 8

Consider the function $f : [0, \frac{π}{2}] \to ℝ$ $given by f (x) = \sin x and g : [0, \frac{π}{2}] \to ℝ$ given by $g (x) = \cos x$ . Show that $f$ and $g$ are one-one functions.

EASY

12th Kerala Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Relations and Functions>Kerala Board-2019>Q 9

Consider the function $f : [0, \frac{π}{2}] \to ℝ$ $given by f (x) = \sin x and g : [0, \frac{π}{2}] \to ℝ$ given by $g (x) = \cos x$ . Is $f + g$ is one-one?why?