Compare two functions.

Categories MATH
Date 07/08/2022
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For the given functions $f:y=\frac{2x^{2}+5x+3}{2x+1}$ and $g:y=5x$ . a)Show that in [1;+∞[ , f(x)≤g(x).

To compare two functions,make their difference.

$f(x)-g(x)=\frac{2x^{2}+5x+3}{2x+1}-5x=\frac{2x^{2}+5x+3-5x(2x+1)}{2x+1}=\frac{2x^{2}+5x+3-10x^{2}-5x}{2x+1}=\frac{-8x^{2}+3}{2x+1}<0$ for x≥1.

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