What does it mean for y to be a function of x?

[Miike012]

Homework Statement

What exactly does it mean when the phrase " y as a function of x" mean?

 

[symbolipoint]

The value of y depends on the value of x. x is an independent variable and you may choose values for x to use in an expression. The result of using each of the acceptable values of x will produce a resulting value for y.

For an expression to be a function, each value of y can have ONE value for x. No two y values have the same x value.

 

[Miike012]

I have this problem in my book that says...
f(x)=2x ( does f(x) mean y as a function of x?)
Then it says
Suppose u is a function of x
How would I re-write the problem?

 

[Miike012]

Would I just write it as...
u = 2x?

 

[eumyang]

Maybe, but once again you're being guilty of NOT stating the entire problem VERBATIM.

I have this problem in my book that says...
f(x)=2x
Then it says
Suppose u is a function of x

Is "f(x)=2x" and "Suppose u is a function of x" part of the same problem? And what does the rest of the problem say?

 

[Miike012]

It says...
Suppose that u is a function of x and
y = cu
then what we believe is that y' = cu'

Then it asks me to prove that
y' = cu' is correct.

 

[Miike012]

Does anyone know?

 

[Borek]

Continues here:

https://www.physicsforums.com/showthread.php?t=463047