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mukesh

Member

Registered: 2010-07-18

Posts: 31

ranfe of function

find the range of function
1)f(x)=sinx+cosx+3
2)f(X)=\x-1\ +\x-2\+\x-3\

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: ranfe of function

hi mukesh,

Answer coming up, so stay on-line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

Hi mukesh

Let's do the first one together.Do you know any formulas for converting the sum of a sin(x) and a cos(x) to a product?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

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Registered: 2010-06-20

Posts: 10,623

Re: ranfe of function

Q1.  So what's the biggest this could be?  sin x and cos x could each be 1, but not at the same time.

This will have a maximum when tanx = 1, so the maximum for Q1 is root 2 + 3

Similarly the minimum will be when tan x = -1 giving a minimum of 3 - root 2.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: ranfe of function

Q2.

I'm assuming those \  \ lines are for 'absolute values'

As x tends to infinity all three absolutes tend to infinity too.

Now, what's the smallest those three bits could be?

Try some critical values.

x = 0

expression = 1 + 2 + 3 = 6

x = 1

expression = 0 + 1 + 2 = 3

x = 2

expression = 1 + 0 + 1 = 2

x = 3

expression = 2 + 1 + 0 = 3

The graph is symmetrical about x = 2 so that's the minimum.

So the range is [2, ∞)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

Here is another way for the first question:

Notice that:

Because the minimum of the sin(x) function is -1 and the maximum is 1,the minimum and maximum of the function

will be -√2 and √2,so when we add the 3 on top we get that the minimum and maximum of your first function are:

Last edited by anonimnystefy (2012-04-22 20:31:57)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

And here is the graph Bob was talking about:

Last edited by anonimnystefy (2012-04-22 22:27:33)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

mukesh

Member

Registered: 2010-07-18

Posts: 31

Re: ranfe of function

thanks from the heart

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

You are welcome.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: ranfe of function

hi mukesh and Stefy,

Sorry, I had to rush away quickly.

Thanks, Stefy for filling in the gaps.  Your Wolfram graph images are not showing for me.

So I've made the three absolutes separately using Sketchpad, and then the combined graph using

http://www.mathsisfun.com/data/function … =-8&ymax=8

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

Hi bob

Wolfram's graphs seem to have unstable links or something.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: ranfe of function

Does it show for you?

Maybe there's part of it only on your machine.  So the rest of us cannot view it.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: ranfe of function

I don't know.After some time it doesn't show me either.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: ranfe of function

(2) Let

Using Triangle Inequality

Where

So

equality hold when

So

So

at

So

Last edited by juantheron (2012-04-23 05:24:17)