Linear relation between non linear functions?

[roineust]

Could there be a linear relation between non linear functions? Can you visualize examples on a graph to help me understand?

 

[Romsek]

[MATH]f(x) = \sqrt{x}\\ g(x) = 2\sqrt{x} = 2f(x)\\ \text{$g(x)$ is linear in terms of $f(x)$ and both are clearly non-linear}[/MATH]

 

[MarkFL]

I'm not sure what you mean, but consider the following non-linear functions:

[MATH]f(x)=x^3-1[/MATH]
[MATH]g(x)=x^2+x+1[/MATH]
Now, what is the quotient:

[MATH]h(x)=\frac{f(x)}{g(x)}[/MATH] ?

 

[roineust]

I'm not sure what you mean, but consider the following non-linear functions:

[MATH]f(x)=x^3-1[/MATH]
[MATH]g(x)=x^2+x+1[/MATH]
Now, what is the quotient:

[MATH]h(x)=\frac{f(x)}{g(x)}[/MATH] ?

It is equal x-1, therefor a linear function, thanks.

 

[roineust]

Is the relation between the 2 following functions linear?

 

[MarkFL]

Is the relation between the 2 following functions linear?

View attachment 16883

The second function implies:

[MATH]\sqrt{1-\frac{v^2}{c^2}}=\frac{L}{L_0}[/MATH]
Substituting that into the first function, we get:

[MATH]T=\frac{T_0}{\dfrac{L}{L_0}}=\frac{L_0T_0}{L}[/MATH]
So, we see they share an inverse relationship, rather than linear.

 

[roineust]

Can you help me understand the difference between a linear and an inverse relation?

 

[Steven G]

Draw a line. Draw any non linear function above it. Draw a non linear function below it. Done.

Do you understand?

You can draw any function that is always positive (y=x^2+1). Then draw any function that is always negative (y=-x^2 -4). Now draw the line y=0 (or y= 1/2 ....). Done.

 

[Steven G]

Based on other responses I guess that I am not understanding this question.

Here is my understanding: Given that g(x) and h(x) are non linear functions find a linear function (linear relation) f(x) such that g(x) < f(x) < h(x) or h(x) < f(x) < g(x).

Someone please enlighten me.

OK, I get it now!

 

[roineust]

The second function implies:

[MATH]\sqrt{1-\frac{v^2}{c^2}}=\frac{L}{L_0}[/MATH]
Substituting that into the first function, we get:

[MATH]T=\frac{T_0}{\dfrac{L}{L_0}}=\frac{L_0T_0}{L}[/MATH]
So, we see they share an inverse relationship, rather than linear.

Is saying that they share an inverse relation rather than a linear relation, mean that dividing these 2 inverse non-linear functions one by the other, will result in a non-linear graph?