Thread: Fonction

Hello Guys

I Need some Help in Fonctions
The function f is set to R:
F (x) = 3x 4x ^ 2 -1/2

1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
-1 And 1

3. Let x = cos (alfa)
Express cos3 (alfa), according to cos (alfa)
2. Determiner solutions of the equation f (x) = 0


my second question for x between 0 and 2pie, solve cos(4x)=sin(2x) {edit : i solved this No need to solve it again lol

and my last question :
Prove that the equation sinx -1/2 = 0
In admits } 0, 2 (pi) {a unique solution

Thanks In Advance

Originally Posted by iceman1

...
and my last question :
Prove that the equation sinx -1/2 = 0
In admits } 0, 2 (pi) {a unique solution

Hello,

if I understand your question right you are looking for the solutions of



Then you get 2 (two) solutions: (see attachment)

Thanks Mate , any help with the First question?? i only solved the first part

Thanks

Originally Posted by iceman1

I Need some Help in Fonctions
The function f is set to R:
F (x) = 3x 4x ^ 2 -1/2

1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
-1 And 1

Probably the reason no one has helped you with it is because the form is strange.

Is this

or

or something else?

Edit: to have 3 roots it's likely a cubic, but I would like verification of the form first.

-Dan

Originally Posted by iceman1

Hello Guys

I Need some Help in Fonctions
The function f is set to R:
F (x) = 3x 4x ^ 2 -1/2

1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
-1 And 1
...

Hello,

you mentioned 3 (three) distinct solutions. So I assume that your function reads:



You have to solve the equation f(x) = 0:

. A product of two factors equals zero if one factor equals zero:

Solve the equations for x. I've got:

These three solutions belong to [-1, 1]

Ah ok Thanks Guys