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  • please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 9 maths textbook solution

please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 9 maths textbook solution

Answers (1)

f(x) is strictly increasing function on R.

Hint:

A function f(x) is strictly increasing on(a,b), if the value off(x) increase with the increase in the value of R.

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:

Here given that,

               f(x)=7 x-3

To prove:

We have to prove that functionf(x)=7 x-3 is strictly increasing function on R.

Solution:

Here given that,

f(x)=7 x-3

Let us considerx_{1},x_{2}\in Rand x_{1}<x_{2}

               x_{1}<x_{2}

Multiplying 7 on both sides,

\Rightarrow 7x_{1}<7x_{2}

Subtracting 3 on both sides,

We get,
\begin{array}{ll} \Rightarrow & 7 x_{1}-3<7 x_{2}-3 \\ \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 R

So, f(x) is strictly increasing function on R.

 

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