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Chapter 12: Q. 20 (page 944)

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

Short Answer

Expert verified

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

Step by step solution

01

Given 

Given that:鈭�f鈭�y=鈭�g鈭�y

02

To find 

We have to find the relationship between f and g.

03

Calculation  

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

We can write them as: gx,y=fx,y+kx, where kxis a function of x.

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