Given:
The function is
[tex]f(x)=x^2+2x+1[/tex]
To find:
The value of [tex]f(x+h)[/tex] in simplified form.
Solution:
We have,
[tex]f(x)=x^2+2x+1[/tex]
Putting [tex]x=x+h[/tex], we get
[tex]f(x+h)=(x+h)^2+2(x+h)+1[/tex]
[tex]f(x+h)=x^2+2xh+h^2+2x+2h+1[/tex]
[tex]f(x+h)=x^2+h^2+2xh+2x+2h+1[/tex]
Therefore, the simplified value of [tex]f(x+h)[/tex] is [tex]x^2+h^2+2xh+2x+2h+1[/tex].
