Question

Ajutor...va rog frumos!!!!
Urgent!!!!!!!!

Answer 1

a)

$(f\circ g)(x)=f(g(x))=f(2x+1)=(2x+1)^2-7(2x+1)+6=4x^2-10x$

b)

$(f\circ g)(x)=0\Rightarrow 4x^2-10x=0\Rightarrow2x(2x-5)=0\Rightarrow x=0\text{ sau }2x-5=0\Rightarrow x=0\text{ sau }x=\displaystyle\frac{5}{2}\\x\in\{0,\frac{5}{2}\}$

c)

$(g\circ f)(x)=g(f(x))=g(x^2-7x+6)=2(x^2-7x+6)+1=2x^2-14x+13$

d)

$(g\circ f)(x)=0\Rightarrow 2x^2-14x+13=0\\\Delta=196-106=92\\\sqrt{\Delta}=2\sqrt{23}\\\displaystyle x_{1,2}=\frac{14\pm2\sqrt{23}}{4}=\frac{7\pm\sqrt{23}}{2}$