Question

Hey everybody!

Could you please try and help me with this?

I would be very grateful if you could!​

Answer 1

`f(x)=|-2x+1|\qquad \qquad \stackrel{domain}{\{-2~~,~~1~~,~~(2)/(3)\}} \\\\[-0.35em] ~\dotfill\\\\ f(-2)=|-2(-2)+1|\implies f(-2)=|4+1|\implies f(-2)=\boxed{5} \\\\\\ f(1)=|-2(1)+1|\implies f(1)=|-2+1| \\\\\\ \qquad f(1)=|-1|\implies f(1)=\boxed{1}`

`f\left( (2)/(3) \right)=\left|-2\left( (2)/(3) \right)+1\right|\implies f\left( (2)/(3) \right)=\left|-(4)/(3)+1\right|\implies f\left( (2)/(3) \right)=\left|(-4+3)/(3)\right| \\\\\\ \qquad \qquad f\left( (2)/(3) \right)=\left|-(1)/(3)\right|\implies f\left( (2)/(3) \right)=\boxed{(1)/(3)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{range}{\{5~~,~~1~~,~~(1)/(3)\}}~\hfill`