Given that:
[tex]f(x)=x^2-5x+1[/tex]Therefore:
[tex]f(t)=t^2-5t+1[/tex]To find f(t+2), we replace t with t+2 in f(t).
[tex]f(t+2)=(t+2)^2-5(t+2)+1[/tex]We can then simplify:
[tex]\begin{gathered} f(t+2)=(t+2)^2-5(t+2)+1 \\ =(t+2)(t+2)-5t-10+1 \\ =t^2+2t+2t+4-5t-10+1 \\ =t^2-t-5 \end{gathered}[/tex]Therefore:
[tex]f(t+2)=t^2-t-5[/tex]