How to solve: If f(x) is even fcn, find range of b. f(x)=[3.5+bsinx] where [] is gif

Abhishekdas

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If f(x) is an even function, then find range of b.
f(x)=[3.5+bsinx] where [] is gif.

I couldn't try anything as I have no idea how to proceed.
 
If f(x) is an even function, then find range of b.
f(x)=[3.5+bsinx] where [] is gif.

I couldn't try anything as I have no idea how to proceed.
please explain that part of the statement.
 
If f(x) is an even function, then find range of b.
f(x)=[3.5+bsinx] where [] is gif.
How does "b" relate to any of the rest of what you've posted? Have you posted one exercise, or two? When you say you "have no idea how to proceed", do you mean that you don't know what "even" and "odd" functions are? Or you're not familiar with trig functions? Or you're not familiar with functions and function notation?

Please reply with specifics, in addition to answering the question in the previous response. Thank you! ;)
 
If f(x) is an even function, then find range of b.
f(x)=[3.5+bsinx] where [] is gif.

I couldn't try anything as I have no idea how to proceed.
Before you or anyone can even start a problem like this you must know what [] and an even function means. Do you know these definitions? Do you know the steps to show if a function is even or not? You can't play the game if you don't know the rules!
 
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Before you or anyone can even start a problem like this you must know what [] and an even function means. Do you know these definitions? Do you know the steps to show if a function is even or not? You can't play the game if you don't know the rules!
OK! I know what even or odd function means.
If a function is even, then f(x)=f(-x). I did try to do the same thing with this question also, but got nothing out of it.
 
[What Does This Mean?]

Before you or anyone can even start a problem like this you must know what [] and an even function means. Do you know these definitions? Do you know the steps to show if a function is even or not? You can't play the game if you don't know the rules!
Ok! So [] means greatest floor function or greatest integer function.
 
Reply

How does "b" relate to any of the rest of what you've posted? Have you posted one exercise, or two? When you say you "have no idea how to proceed", do you mean that you don't know what "even" and "odd" functions are? Or you're not familiar with trig functions? Or you're not familiar with functions and function notation?

Please reply with specifics, in addition to answering the question in the previous response. Thank you! ;)
I know quite a bit about trig and functions. I did try to do f(x)=f(-x), but it didn't work out.
 
becoz [3.5+bsinx] is not equal to f(x) = 3.5 + b * sin(x)
You answered that f(x) is not even because \(\displaystyle \lfloor{f(x)}\rfloor \ne f(x)\).

It's true that f(x) is not even, but I don't think your reason why is valid.

f(x) is not even because sin(x) is not even.



Consider the following function g.

g(x) = 3.5 + b*cos(x)

This is an even function because cos(x) is an even function.

If we let b = 1, for an example, here's the graph of \(\displaystyle g(x)\) and \(\displaystyle \lfloor{g(x)}\rfloor\).

\(\displaystyle \lfloor{g(x)}\rfloor \ne g(x)\), yet g(x) is even. :cool:
 

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I don't get it. Isn't f(x)= [3.5+bsinx]. Kindly elaborate.
Yes, that is the definition of f(x). That can't be questioned as it was given!

YOU said that a function f(x) is defined to be an even function if f(x) = f(-x), yet you claimed, as mbot pointed out, that f(x) is not even because
[f(x)] is not equal to f(x). Where did this definition come from????

You want to verify whether or not f(x)=f(-x), that is whether or not [3.5+bsin(x)] = [3.5+bsin(-x)] . When is this true? Remember that your answer should depend on b
 
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Hmmm, how about |b|< 1/2 ???????
You are correct for OP.

However, I was trying to "nudge" OP in that direction by assuming a simpler function (removing GIF operation).
 
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