If f(x) = x squared - 6x + 1, find f(x-h) - f(x)?

Question

I don't need the answer (it would be nice), just how to solve it.

Answer 1

lets go through some basic functions first. using your example:
f(x) = x squared - 6x + 1

to find f(2) we substitute all x with a 2:
f(2) = 2^2 - 6(2) + 1 = -7

to find f(-1) we substitute all x with a -1:
f(-1) = -1^2 - 6(-1) + 1 = 8

to find f(b) we substitute all x with a b:
f(b) = b^2 - 6b + 1

so you see where i'm going with this? anything that is in the brackets will replace the x.

so if i wanna find f(2) + f(-1) that would be:
[ 2^2 - 6(2) + 1 ] + [ -1^2 - 6(-1) + 1 ]
= -7 + 8
= 1.

so back to your question:
f(x-h) - f(x).

to solve this we fist need to determine what is f(x-h), and that would simply be substituting all x with (x-h):

f(x-h) = (x-h)^2 - 6(x-h) + 1

we already know what f(x) is. with these two information, we can easily solve for f(x-h) - f(x):

f(x-h) - f(x) = [ (x-h)^2 - 6(x-h) + 1 ] - [ x^2 - 6x + 1 ]

all you have to do is expand and simplify. remember though to be really careful as many make a whole lotta careless mistakes when dealing with these.

hope you now have a better understanding of functions and of these types of questions. have fun!

Answer 2

You might actually be wanting to find f(x + h) - f(x) if this is related to something in calculus.

f(x) = x^2 – 6x +1
f(x + h) = (x + h)^2 – 6(x + h) + 1
= x^2 + 2xh + h^2 – 6x – 6h + 1
The difference is
f(x +h) – f(x) = x^2 + 2xh + h^2 – 6x – 6h + 1 – x^2 + 6x – 1
= 2xh + h^2 – 6h

This can be check against the derivative, but I assume that you can do that on your own.

Answer 3

f(x) = x^2 - 6x + 1

f(x - h) means 'replace every "x" with "x - h"

f(x - h) = (x - h)^2 - 6(x - h) + 1
f(x) = x^2 - 6x + 1

f(x - h) - f(x) = (x - h)^2 - 6(x - h) + 1 - (x^2 - 6x + 1)
=x^2 - 2hx + h^2 -6x + 6h + 1 - x^2 + 6x - 1
=(x^2 - x^2) + (-2hx - 6x + 6x) + (h^2 + 6h + 1 - 1)
=(0) + (-2hx) + (h^2 + 6h)
= -2hx + h^2 + 6h

The key part to this question is to factor out an "h" in the expression
-2hx + h^2 + 6h = h*(-2x + h + 6)

Answer 4

f(x) = x^2 - 6x + 1

f(x - h) = (x - h)^2 - 6(x - h) + 1
f(x - h) = ((x - h)(x - h)) - 6x + 6h + 1
f(x - h) = (x^2 - xh - xh + h^2) - 6x + 6h + 1
f(x - h) = x^2 - 2xh + h^2 - 6x + 6h + 1

f(x - h) - f(x) = (x^2 - 2xh + h^2 - 6x + 6h + 1) - (x^2 - 6x + 1)
f(x - h) - f(x) = x^2 - 2xh + h^2 - 6x + 6h + 1 - x^2 + 6x - 1
f(x - h) - f(x) = 2xh + h^2 - 6x + 6h + 6x
f(x - h) - f(x) = 2xh + h^2 + 6h
f(x - h) - f(x) = h^2 + 2xh + 6h
f(x - h) - f(x) = h^2 + 2(x + 3)h

ANS : h^2 + 2xh + 6h

Answer 5

you put x-h for x in f(x) and expand this gives f(x-h)
then subtract f(x) from f(x-h) to get the answer

Answer 6

f(x)=(x^2-6x+1)
f(x-h)=(x-h)^2-6(x-h)+1
=x^2-2xh+h^2-6x+6h+1
f(x-h)-f(x)=h^2-2xh+6h