Theorem 2 If a quantity f is a function of x, y, and z, and a relation exists amongst x, y and z, then f is a function of any two of x, y, and z.

ƒ = ƒ(x, y, z)

1.84

or,

x = x(y, z)

1.85

x = x(ƒ, y)

1.86

x = x(ƒ, z)

1.87

If x = x(ƒ, y)

1.88

Similarly, if y = y(ƒ, z)

1.89

From Eqs. (1.88) and (1.89), we have

1.90

or,

1.91

If ,x = x(ƒ, z) then

1.92

From Eqs. (1.91) and (1.92),

1.93

Eq. (1.93) can be rewritten as

1.94