Question

Fie functiile f,g :R→R,
f(x)=_x-7_ , g(x)=3x-1
2
a)Aflati zerourile functiilor f si g
b)Pentru ce valori reale ale lui x , f(x)>_(este mai mare , egal)g(x)?

Answer 1

a) Zerourile:
$f(x)=0 =\ \textgreater \ \frac{x-7}{2} =0 \ \textless \ =\ \textgreater \ x-7=0 \ \textless \ =\ \textgreater \ x=7 \\ g(x)=0 =\ \textgreater \ 3x-1=0 \ \textless \ =\ \textgreater \ 3x=1\ \textless \ =\ \textgreater \ x= \frac{1}{3}$
b) 
$f(x) \geq g(x) \geq \frac{x-7}{2} \geq 3x-1|*2 \\ x-7 \geq 2(3x-1) \\ x-7 \geq 6x-2 \\ x-6x \geq -2+7 \\ -5x \geq 5 \\ x \leq -1$ 
x apartine (- infinit, - 1]