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Chapter 12: Q. 19 (page 944)

Let f(x, y) and g(x, y) be functions of two variables with the property that 鈭�f鈭�x=鈭�g鈭�xfor every point x,y鈭�R2. What is the relationship between f and g?

Short Answer

Expert verified

The relationship is:gx,y=fx,y+ky, where kyis a function of y.

Step by step solution

01

Given 

Given that:鈭�f鈭�x=鈭�g鈭�x

02

To find 

We have to find the relationship between f and g.

03

Calculation 

If 鈭�f鈭�x=鈭�g鈭�xthen we can say that only x part of the functions are the same in both functions. And x is independent of y.

We can write them as: gx,y=fx,y+ky, wherekyis a function of y.

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