Question

determine f(x)-f(a)/x-a, x does not equal a given f(x)=x^4-16

Answer 1

to get f(a) u just replace 'x' with 'a' in f(x), what u get ?

Answer 2

In other words, he means to do this:

\[\frac{f(a) - f(a)}{a - a}\]

(I think)

You don't really need a function to see that this is not going to work.

Answer 3

why is denominator a-a ? it remains x-a

Answer 4

Because it says to determine that x does not equal a

Answer 5

Which implies to go ahead and let x = a and see what happens

Answer 6

im supposed to plug in the f(x)=x^4-16 so what i have is x-16-f(a) over x-a and to determine how that does not equal a....so how do i do that?

Answer 7

Even if you used the function, you would still get the same result which is 0/0 indeterminate

Answer 8

f(x)-f(a) = x^4-16 - (a^4-16)
did u get this part ?

Answer 9

If you let x = a, you would have this:

a^4 - 16 - (a^4 - 16) in the numerator

Answer 10

i let x=a only to get f(a) part, nowhere else, x should be replaced by a
then f(a) = a^4-16
i just put that in f(x)-f(a)

Answer 11

If you don't replace x with a then you won't be following the problem the way it is intended.

Answer 12

The way it works is if you have x = a, then you have the point (a, f(a)). There's no way around that

Answer 13

Everything has to be consistent

Answer 14

my solution :
f(x)-f(a) = x^4-16 - (a^4-16) = x^4-a^4
so
(f(x)-f(a))/(x-a) = (x^4-a^4 )/ (x-a)
= (x^2-a^2)(x^2+a^2) / (x-a)
= (x-a)(x+a)(x^2+a^2) / (x-a)
=(x+a)(x^2+a^2)

Answer 15

Did you prove that x does not equal a?

Answer 16

i think ' x does not equal a' is a given information, thats why i could cancel x-a from numerator and denominator

Answer 17

I see. Yeah, you're right.

Answer 18

ok thank you for the help i have another question..... f(x)=Ix-2I and i need to know if the function is even odd or neither how do i do that

Answer 19

Replace x with -x

Answer 20

so when i do that it would be I-x-2I but then when it comes out of the absolute value will it be x+2 or x-2??

Answer 21

After that, you have to simplify and determine if you still get |x -2|. If you do, then it is an even function. If you don't, then it is an odd function.

Answer 22

ok but im unsure of how it simplifies to....would it be x+2 or x-2 because i know absolute value changes pos to neg but what if it is that equation in the absolute value

Answer 23

f(-x)
= |-x-2|
=|-(x+2)|
= x + 2

x - 2 ≠ x + 2
therefore, the function is odd

Answer 24

odd ?

Answer 25

wouldn't it be neither odd, nor even ?

Answer 26

Find f(-x)
by replacing x in f(x) by -x.
If f(-x) = f(x), then the function is even
If f(-x) = -f(x), then the function is odd
else neither.

Answer 27

It's been a while since I did this, sorry.

Answer 28

i think hes right about it being odd because when u have I-xI=x and I-2I=2 therefore u get x+2 and it is the opposite of x-2 so it is odd...i just needed to verify that it would come out as x-2 Thanks again!!

Answer 29

its ok i am the same im helping a friend study for her class

Answer 30

No, @hartnn is right. Those are the rules for even and odd functions that he posted.

Answer 31

since u don't get f(-x) as |x-2| (even) or -|x-2| (odd)
hence. the function is neither

Answer 32

im confused now so it isnt even or odd....its neither? how?

Answer 33

dont u get I-x-2I so when u solve it would come out to be x+2?

Answer 34

if the function would have been even, u get f(-x) = f(x) = |x-2|
but u don't get this.
similarly
if the function would have been odd, u get f(-x) = -f(x) = -|x-2|
but what u actually get is |-(x+2)| which is neither |x-2| nor -|x-2|

Answer 35

i told u how to find f(a)
did u understand that and could u find f(a) ?