Chapter 12: Q 5. (page 915)

Let $f : R^{3} \to R$ be a function of three variables. Explain why the graph of f is a subset of $R^{4}$ .

Short Answer

Expert verified

The graph of f is a subset of $R^{4}$ as it is plotted using four axes: x, y, z and w.

Step by step solution

Step 1. Given information

Function is $f : R^{3} \to R$

Step 2. Explanation

A graph is a graphic representation that shows between input and output variables.

The input and output values are used to plot the graph of a function.

For the function $w = f (x, y, z)$ , graph is to be plotted between four variables, ' $x, y, z, w$

Thus, the graph will have four axes to plot.

This is the definition of $R^{4}$

Hence, the graph of f must be a subset of $R^{4}$

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Let $f : R^{3} \to R$ be a function of three variables. Explain why the graph of f is a subset of $R^{4}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Let f:R3→Rbe a function of three variables. Explain why the graph of f is a subset of R4.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Let $f : R^{3} \to R$ be a function of three variables. Explain why the graph of f is a subset of $R^{4}$ .