Problem

Find the indicated value of the function $f(x, y, z)=2 x-5 y^{2}+2 z^{3}-6$
\[
f(1,-3,1)
\]
\[
f(1,-3,1)=
\]

Answer

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Answer

Therefore, the final answer is \(\boxed{38}\).

Steps

Step 1 :The function f(x, y, z) is given as \(f(x, y, z)=2 x-5 y^{2}+2 z^{3}-6\). We need to find the value of the function at the point (1,-3,1). This can be done by substituting the values of x, y, and z into the function.

Step 2 :After substituting the values, we get \(f(1,-3,1)=2(1)-5(-3)^{2}+2(1)^{3}-6\).

Step 3 :Solving this, we get \(f(1,-3,1)=2-5(9)+2-6\).

Step 4 :Further simplifying, we get \(f(1,-3,1)=2-45+2-6\).

Step 5 :Finally, we get \(f(1,-3,1)=38\).

Step 6 :Therefore, the final answer is \(\boxed{38}\).

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