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please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 3 maths textbook solution

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f(x)=ax+bis an increasing function on R


               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} \epsilon \left ( a,b \right ).


               f(x)=ax+b , wherea,bare constant and a>0

To prove:

               f(x)=ax+b is an increasing function on R.


Let x_{1},x_{2}\epsilon RSuch that x_{1}<x_{2}


\begin{aligned} &x_{1}<x_{2} \\ &\Rightarrow \quad a x_{1}<a x_{2} \quad[\because a>0] \end{aligned}         

\Rightarrow \quad a x_{1}+b<a x_{2}+b    [Given that b is constant]

\Rightarrow \quad f\left(x_{1}\right)<f\left(x_{2}\right)

Thus, f(x)=ax+b is an increasing function on R.

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