Question

Please show all work

f(x)=x^2+2x+1
find f(x+h) and simplify

Answer 1

Any ideas?

Answer 2

I'm thinking something around

x^2+2x+1+h

Answer 3

f(x+h) means the output you will get if you input (x+h) in the function
So just replace the x's in the function with (x+h)

Answer 4

Hint: replace ALL the x's with x + h

Answer 5

Wherever you see an x put a x+h.

Answer 6

You wrote f(x) + h

Answer 7

so now I have

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

Answer 8

The x^2 should be (x+h)^2

Answer 9

Apply algebraic identity on the first term and expand the second term
\[\large\rm (x+h)^2+2(x+h)+1 \]

Answer 10

or you can make it using that f(x) = x^2 +2x +1 = (x+1)^2

and now just substitute the (x+h) in place of x inside these parentheses and square this

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

Answer 11

@skullpatrol do you agree this please ?

Answer 12

Your method is valid @jhony9 but not "easy" to understand for a beginner :-)

Answer 13

@jhonyy9 Your representation is accurate. But still the question requires simplifying so just by simplifying your expression will give her the answer

Answer 14

thank you Faiq

Answer 15

I kinda get it

Answer 16

so now I have to simplify right?

Answer 17

Yes

Answer 18

ty. skull to you too

Answer 19

@DiamondAnon2 be sure to use lots of parentheses (x+h) is treated as one thing in f(x+h)

Answer 20

okay! thanks all of you :)

Answer 21

Thanks for trying to learn :-)