Answer:
[tex]f(x+2)=x^2+4x+11[/tex]
Step-by-step explanation:
In [tex]f(x)=x^2+7[/tex], for all values of [tex]x[/tex], we substitute [tex]x[/tex] (what is in the parentheses) into [tex]x^2+7[/tex] to output a [tex]y[/tex] value.
In [tex]f(x+2)[/tex], the term [tex](x+2)[/tex] is in the parentheses. Therefore, substitute [tex](x+2)[/tex] for [tex]x[/tex] in [tex]x^2+7[/tex] to find [tex]f(x+2)[/tex]:
[tex]f(x+2)=(x+2)^2+7[/tex]
Expand using [tex](a+b)^2=a^2+2ab+b^2[/tex],
[tex]f(x+2)=x^2+4x+4+7[/tex]
Combine like terms:
[tex]\boxed{f(x+2)=x^2+4x+11}[/tex]
