The function given in the question is
[tex]f(x)=x^2-2x+1[/tex]
The question asks to find the expression for
[tex]f(a+2)[/tex]
To get the expression for f(a+2), we will substitute the value of x = a+2
By substitution, we will have
[tex]\begin{gathered} f(x)=x^2-2x+1 \\ f(a+2)=(a+2)^2-2(a+2)+1 \end{gathered}[/tex]
Expanding the brackets, we will have
[tex]\begin{gathered} f(a+2)=(a+2)^2-2(a+2)+1 \\ f(a+2)=(a+2)(a+2)-2a-4+1 \\ f(a+2)=a(a+2)+2(a+2)-2a-3 \\ f(a+2)=a^2+2a+2a+4-2a-3 \\ f(a+2)=a^2+4a-2a+4-3 \\ f(a+2)=a^2+2a+1 \end{gathered}[/tex]
Therefore,
The expression for f(a+2) is
f(a+2) = a² + 2a + 1
