Question

F(x) = x2 + 2x + 1, find f(x + h) and simplify.

Answer 1

Given:

The function is

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

To find:

The value of $f(x+h)$ in simplified form.

Solution:

We have,

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

Putting $x=x+h$, we get

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

$f(x+h)=x^2+2xh+h^2+2x+2h+1$

$f(x+h)=x^2+h^2+2xh+2x+2h+1$

Therefore, the simplified value of $f(x+h)$ is $x^2+h^2+2xh+2x+2h+1$.