Question

Hello , please see attached and can you give a Answer for this .

Answer 1

The function given in the question is

$f(x)=x^2-2x+1$

The question asks to find the expression for

$f(a+2)$

To get the expression for f(a+2), we will substitute the value of x = a+2

By substitution, we will have

$\begin{gathered} f(x)=x^2-2x+1 \\ f(a+2)=(a+2)^2-2(a+2)+1 \end{gathered}$

Expanding the brackets, we will have

$\begin{gathered} f(a+2)=(a+2)^2-2(a+2)+1 \\ f(a+2)=(a+2)(a+2)-2a-4+1 \\ f(a+2)=a(a+2)+2(a+2)-2a-3 \\ f(a+2)=a^2+2a+2a+4-2a-3 \\ f(a+2)=a^2+4a-2a+4-3 \\ f(a+2)=a^2+2a+1 \end{gathered}$

Therefore,

The expression for f(a+2) is

f(a+2) = a² + 2a + 1