Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1, question 1 maths textbook solution

please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 1 maths textbook solution

Answers (1)

Answer:

               f(x) is increasing in(0,\infty )

Hint:

A function f(x) is said to be a increasing function on(a, b), if x_{1}<x_{2} \Rightarrow f\left(x_{1}\right)<f\left(x_{2}\right) for all x_{1}, x_{2} \in(a, b).

Given:

               f(x)=\log _{e} x

To prove:

Function f(x)=\log _{e} x  is increasing on (0,\infty )

Solution:

Let us consider x_{1}, x_{2} \in(0, \infty) and x_{1} < x_{2}

Then,    

               x_{1} < x_{2}

Taking loge on both sides,

\Rightarrow \quad \log _{e} x_{1}<\log _{e} x_{2}

\Rightarrow \quad f\left(x_{1}\right)<f\left(x_{2}\right) for all x_{1}, x_{2} \in(0, \infty)

So, f(x) is increasing in (0,\infty )

Posted by

Info Expert 29

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question