Consider the given functions,
[tex]\begin{gathered} f(x)=x^2-4x+6 \\ g(x)=-3x+1 \end{gathered}[/tex]
Solve for the composite function as follows,
[tex]\begin{gathered} g\circ f(x) \\ =g\mleft(f\mleft(x\mright)\mright) \\ =g\mleft(x^2-4x+6\mright) \\ =-3(x^2-4x+6)+1 \\ =-3x^2+12x-18+1 \\ =-3x^2+12x-17 \end{gathered}[/tex]
Thus, the required composit function is obtained as,
[tex]g\circ f(x)=-3x^2+12x-17[/tex]
