In order to be continuous everywhere, we only need to satisfy continuity at [tex]x=10[/tex]. For that to happen, we need to have
[tex]\displaystyle\lim_{x\to10^-}f(x)=\lim_{x\to10^+}f(x)=f(10)[/tex]
By the function's definition, [tex]f(10)=2(10)-2=18[/tex]. Compute the limits:
[tex]\displaystyle\lim_{x\to10^-}f(x)=\lim_{x\to10}2x-2=18[/tex]
[tex]\displaystyle\lim_{x\to10^+}f(x)=\lim_{x\to10}-8x+b=-80+b[/tex]
So we must have
[tex]18=b-80\implies b=98[/tex]
