Q 11. - Calculus

Question

Let w = f(x, y, z) be a function of three variables. Explain why the two sets {(x, y, z) | (x, y, z, w) ∈ Graph( f )} and Domain( f ) are identical.

Step-by-Step Solution

Answer

Two sets {(x, y, z) | (x, y, z, w) ∈ Graph( f )} and Domain( f ) are identical as both have three input variables.

Step 1. Given information

Two sets are {(x, y, z) | (x, y, z, w) ∈ Graph( f )} and Domain( f ) 

Step 2. Explanation

The graph must be plotted between two variables, 'x, y, z and w ', for the function w=f(x, y, z).

As a result, there will be three axes to plot on the graph. This implies that f's graph must be a subset of $R^3$. (x, y, z, w) will be a subset of each point on the graph.

A function's domain is the set of input variable values.

There are three input variables in each point (x, y, z, w), whose values determine the domain set of functions. (x, y, z) will be used to denote each input.

As a result, the sets {(x, y, z) | (x, y, z, w) ∈ Graph( f )} and Domain( f ) are identical.