how does this function work? f(x)....?

Question

i need to find f(x+h)
with the following:
f(x)=6x+2

it is to my understanding that I need to replace the X in the original function with the function of x they are providing me with, thus:

f(x)=6x+2
f(x+h)= 6x+2+h

but the answer in the book is: 6x+6h+2...
and i can't understand why....

Answer 1

You replace "x" with "x+h"

So you get f(x+h)=6(x+h)+2

6x+6h+2

The right answer

Answer 2

replace all x's in f(x) = 6x + 2 with x+h
therefore...
f(x+h) = 6(x+h) + 2
f(x+h) = 6x + 6h +2

Answer 3

the book is right you have to do this
from f(x)=6x+2
f(x+h)=6(x+h)+2
=6x+6h+2

Answer 4

When you replace the x in the function with x + h you get
6(x + h) + 2
or 6x + 6h + 2

Answer 5

f(x) = 6x + 2
Now every x becomes an x + h:-
f(x + h) = 6(x + h) + 2 = 6x + 6h + 2
If you wished to find the derivative, f `(x):-
f `(x) = lim h->0 [f(x + h) - f(x)] / h
f `(x) = lim h->0 [6x + 6h + 2 - 6x - 2] / h
f `(x) = lim h->0 [ 6h ] / h
f `(x) = 6 (as expected)

Answer 6

no the x+h replaces the x
and the x in the problem f(x)=6x+2 is linked to the 6

f(x+h)= 6(x+h) +2
now distribute

also the guy before me is kinda right. it would turn out to be
2(3x+3h+1)

Answer 7

um, when it says f(x+h), doesn't mean you just add h in the end, in fact, you have to substitude the original x with what f(x) is, which in this case, (x+h)

so we have f(x+h) = 6(x+h)+2

distribute, we have,
6x+6h+2

or simply
3x+3h+1

Answer 8

f(x)=6x+2

f(x+h)=6(x+h)+2
f(x+h)=6x+6h+2