Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.
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Answer
Here, $\text{f}(\text{x})=7\text{x}-3$ Let $\text{x}_1,\text{x}_2\in\text{R}$ such that $\text{x}_1<\text{x}_2.$ Then, $\text{x}_1<\text{x}_2$ $\Rightarrow7\text{x}_1<7\text{x}_2$$[\because\ 7>0]$ $\Rightarrow7\text{x}_1-3<7\text{x}_2-3$ $\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2)$ $\therefore\ \text{x}_1<\text{x}_2\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2),\forall\ \text{x}_1,\text{x}_2\in\text{R}$ So, f(x) is strictly increasing on R.
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