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  • please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 5 maths textbook solution

please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 5 maths textbook solution

Answers (1)

f(x) is a decreasing function.

Hint:

               A function f(x) is said to be a decreasing 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) \text { . }

Given:

Here given that,

               f(x)=\frac{1}{x}

To prove:

               f(x)=\frac{1}{x} is a decreasing function on (0,\infty )

Solution:

Let x_{1}, x_{2} \in(0,\infty ) Such that x_{1}< x_{2}

Then,
         \begin{array}{ll} & x_{1}<x_{2} \\ \Rightarrow & \frac{1}{x_{1}}>\frac{1}{x_{2}} \\ \Rightarrow & f\left(x_{1}\right)>f\left(x_{2}\right) \end{array}

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

So, f(x)is a decreasing function.

 

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