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`.