Let F(x, Y, Z)= Ax + by + Cz

question 46

Essay

Let f(x, y, z)= ax + by + cz + d be a linear function of three variables, for constants a, b, c and d.
Given that some of the cross sections of f are f(x, 1, 1)= 0 + 4x, f(0, y, -3)= 4 + 4y,
and f(1, 1, z)= 6 - 2z, find a formula for f.

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