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  • 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 )

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