Question

Fie functiile f, g:R→R, f(x)=5-x supra 2, g(x)=5x+1
a) Aflati zerourile functiilor f si g
b)Pentru ce valori reale ale lui x,f(x)≥g(x)?

Answer 1

[tex]\bold{a)}~~f(x)= \frac{5-x}{2} \\\\ f(x)=0 \Leftrightarrow \frac{5-x}{2} =0 \Leftrightarrow 5-x=0 \Leftrightarrow x=5\\\\\\ g(x)=5x+1\\\\g(x)=0\Leftrightarrow5x+1=0\Leftrightarrow5x=-1\Leftrightarrow x= -\frac{1}{5} \\\\ \bold{b)}~~f(x) \geq g(x)\\\\Deci\\\\ \frac{5-x}{2} \geq 5x+1\Leftrightarrow5-x \geq 10x+2\Leftrightarrow-x-10x \geq 2-5\Leftrightarrow\\\\ \Leftrightarrow-11x \geq -3/\cdot(-1)\Leftrightarrow11x \leq 3\Leftrightarrow x \leq \frac{3}{11} \Leftrightarrow~ \in (-\infty; \frac{3}{11} ][/tex]