Define the following functions:f(x, y, z) = xy + yz + zxg(x, y, z) = x2y + y2z + z2x andh(x, y, z) = 3 xyzQ.Find the value of the following expressions:37. h[f(2, 3, 1), g(3, 4, 2), h(1/3, 1/3, 3)]a)0b)23760c)2640d)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Calculation:

Given functions:
- f(x, y, z) = xy yz zx
- g(x, y, z) = x^2y y^2z z^2x
- h(x, y, z) = 3xyz

Substitute values into functions:
- f(2, 3, 1) = 2*3 + 3*1 + 1*2 = 6 + 3 + 2 = 11
- g(3, 4, 2) = 3^2*4 + 4^2*2 + 2^2*3 = 36*4 + 16*2 + 4*3 = 144 + 32 + 12 = 188
- h(1/3, 1/3, 3) = 3*(1/3)*(1/3)*3 = 3*(1/9)*3 = 1

Plug the values into h function:
- h[f(2, 3, 1), g(3, 4, 2), h(1/3, 1/3, 3)] = h(11, 188, 1) = 3*11*188 = 3*2056 = 6168

Answer:
Therefore, the value of h[f(2, 3, 1), g(3, 4, 2), h(1/3, 1/3, 3)] is 6168. So, the correct option is (C) 2640.

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