Algebra of Functions: Arithmetic

Question

Given: f(x) = x² + 2x + 1, find f(x + h) and simplify

could you explain where the h comes from

Answer 1

H is just a general notation for an amount that x is increased by. You will use this later when you learn about derivatives in calculus.

To find f(x+h) just substitute (x+h) for x

so we have f(x+h)= (x+h)^2 + 2(x+h) +1 = x^2 +2xh +h^2 +2x+2h+1

Answer 2

Hi,

Given: f(x) = x² + 2x + 1, find f(x + h) and simplify

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

= x^2 + 2xh + h^2 + 2x + 2h +1

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

The goal of this question is:

1) you can replace any number or expression instead of x, x is input of your function, then find out put.

2) h comes from ???? in fact h is a number that no matter what it is. But in the future you will learn h is a very small number.

3) if above explanation is make sense, now you figure out if I ask you what f( Laken) is. ( funny)

in fact: f( Laken) = ( Laken)^2 + 2 ( Laken) + 1 this expression can be a lot of meaning, for example may be it is: your schedule, your time that you are studying, or any thing depends on you.

I hope it is useful, please let me know if you have any question.

Minoo