please help me with The f(x) notation.?

Question

please include a detailed solution. thanks.
Problem:
if f(x)=2x to the 2nd power - 1,
find:
1. f(2x)-f(-x)
2. f(x+1)
thanks

im sorry. not like this:
(2x)2
but like this:
2x2 (2x squared)

yahoo doesnt have superscript font format. x is squared.

2x2

Answer 1

I seem to be the first with the correct solution... the confusion is obviously the notation. If you can't type superscripts easily, you can always use ^ to mean exponentiation. (Or Alt-253 on a PC keypad will get you a superscript ²).

The solution is to simply substitute x in your equation with whatever is put inside the parentheses. It can be confusing if that includes another equation, but it is still simple substitution.

Given:
f(x) = 2(x^2) -1

f(2x) = 2((2x)^2) - 1
f(2x) = 2(4(x^2)) - 1
f(2x) = 8(x^2) -1
f(-x) = 2(-x^2) - 1
f(-x) = 2(x^2) - 1

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

f(x+1) = 2((x+1)^2) - 1
f(x+1) = 2(x^2 + 2x + 1) - 1
f(x+1) = 2x^2 + 4x + 2 - 1
f(x+1) = 2x^2 + 4x + 1

So your answers are:
1) 6x^2
2) 2x^2 + 4x + 1

Written using Alt-253 for the exponent, the answers are:
1) 6x²
2) 2x² + 4x + 1

Answer 2

Is your function f(x)=x², f(x)=(2x)²
or f(x)=2x²-1? You were not clear?
So, I'll solve all three of these:
f(x)=x², f(x)=(2x)² & f(x)=2x²-1?
After this, you should be able to do any of these type of eqs.
----
Assuming you meant f(x)=2x²-1
1) f(2x)-f(-x)=
f(2x)=2(2x)²-1=8x²-1
f(-x)=2(-x)²-1=2x²-1
f(2x)-f(-x)=8x²-1-2x²+1
f(2x)-f(-x)=6x²
-----
2)f(x+1)=
f(x+1)=2(x+1)²-1
f(x+1)=2(x²+2x+1)-1
f(x+1)=2x²+4x+2-1
f(x+1)=2x²+4x+1
===============
or Is your function this?
f(x)=x² ?
-----------------
1) f(2x)-f(-x)=
since f(x)=x² =>
f(2x)=(2x)²=4*x²
f(-x)=(-x)²=x² =>
f(2x)-f(-x)=4x²-x²=3x²
---------------
2) f(x+1)=(x+1)²
f(x+1)=x²+2x+1
===========
Alternatively did you mean the funct to be this?
f(x)=(2x)² ?
If so, follow the same steps that I did for the simpler function above & get answers. It's very easy.
case where:
f(x)=(2x)²
----------
1) f(2x)-f(-x)=
f(2x)=(2*2x)²=(4x)²=16*x²
f(-x)=(-2x)²=4*x²
f(2x)-f(-x)=16 x² - 4 x²
f(2x)-f(-x)=12 x²
-------------
2)f(x+1)=(2(x+1))²
f(x+1)=4*(x+1)²
===================
NOTE
superscript power is alt 253 using keyboard.
x²
The 2x & your explaination of
(2x)2 isn't clear.
To raise to a power on a keyboard you use ^. Example x^2.
To mult use * instead of x, since by using the x, you are confusing the algebraic eqs that use the variable x.
===================

Answer 3

f(x) = 2x^2 – 1

f(2x) = 2*(2x)^2 – 1 = 2 * (4x^2) – 1 = 8x^2 – 1
f(-x) = 2 * (-x)^2 – 1 = 2x2 – 1
Therefore f(2x) – f(-x) = (8x^2 – 1) – (2x^2 – 1) = 6x^2

f(x+1) = 2 * (x+1)^2 – 1 = 2 * (x2 +2x + 1) – 1 = 2x2 + 4x + 2 – 1 = 2x^2 + 4x + 1

Answer 4

f(x) = 2x² - 1

1.
You know that f(x) = 2x² - 1, and to get f(2x) substitute 2x to all x's in the function. Likewise, substitute -x or x + 1 to the function f to get f(-x) or f(x + 1), respectively. Thus,
f(2x) = 2(2x)² - 1 = 2(4x²) - 1 = 8x² - 1
f(-x) = 2(-x)² = 2x² - 1
f(2x) - f(-x) = 8x² - 1 - (2x² - 1) = 6x²

2.
f(x + 1) = 2(x + 1)² - 1 = 2(x² + 2x + 1) - 1 = 2x² + 4x + 1


(NoteL to get exp. ² or ³, Hold Alt and type in numpad 02226 and 02227, respectively!)
^_^^_^

Answer 5

first the sentence "to the 2nd power - 1" is confusing

but instead lemme try:
f(2x)-f(-x)
now let 2x = X
& -x = Y
then (1) becomes:
f(X)-f(Y) =
2X-2Y

now put X=2x 7 Y=-x
=> 2(2x) - 2(-x) = 4x +2x = 6x Ans.

now2.
f(x+1) = 2(x+1)
=2x + 2 Ans.

Answer 6

f(x) = 2x^2 - 1

1.)
f(2x) = 2(2x)^2 - 1 = 2(4x^2) - 1 = 8x^2 - 1
f(-x) = 2(-x)^2 - 1 = 2x^2 - 1

f(2x) - f(-x) = (8x^2 - 1) - (2x^2 - 1) = 8x^2 - 1 - 2x^2 + 1 = 6x^2

------------------------------

2.)
f(x + 1) = 2(x + 1)^2 - 1
f(x + 1) = 2((x + 1)(x + 1)) - 1
f(x + 1) = 2(x^2 + x + x + 1) - 1
f(x + 1) = 2(x^2 + 2x + 1) - 1
f(x + 1) = 2x^2 + 4x + 2 - 1
f(x + 1) = 2x^2 + 4x + 1

Answer 7

1. f(2x)-f(-x)=> 2(2x) - (-2x)=>4x+2x=>6x
2. f(x+1)=>2(x+1)=>2x+2
Got it