Functions of several variables: Basic concepts and visualization
Converting a relation into a functional relationship
In the relationship \(\displaystyle y=\frac{7x+4z}{-3x+5z}\) you immediately see that \(y\) is a function of \(x\) and \(z\).
But is \(z\) also a function of \(x\) and \(y\)? And, if so, what is the function definition?
In other words, can you express \(z\) in \(x\) and \(y\), in the form \(z=\mathrm{formule\;in\;} x\mathrm{\;and\;}y\).
You can also reach the solution by increments entering in the form of equations:
Then you see if you are still on track, but in the end you must get to the equation in the form \(z=\ldots\).
But is \(z\) also a function of \(x\) and \(y\)? And, if so, what is the function definition?
In other words, can you express \(z\) in \(x\) and \(y\), in the form \(z=\mathrm{formule\;in\;} x\mathrm{\;and\;}y\).
You can also reach the solution by increments entering in the form of equations:
Then you see if you are still on track, but in the end you must get to the equation in the form \(z=\ldots\).
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