Q 12. - Calculus

Question

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

Step-by-Step Solution

Answer

Two sets {w | (x, y, z, w) ∈ Graph( f )} and Range( f ) are identical as both have one output variable.

Step 1. Given information

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

Step 2. Explanation

A graph is to be produced 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 $R^4$. (x, y, z, w) will be a subset of each point on the graph.

The output variable range of a function is the set of values.

One output variable determines the range set of functions in each point (x, y, z, w). z will be used to identify each output.

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