Problem

Let $f(x, y)=2^{x}+9 x y$, find $f(0,-3), f(-3,2)$, and $f(3,2)$.
$f(0,-3)=\square$ (Simplify your answer.)
$f(-3,2)=\square$ (Simplify your answer.)
$f(3,2)=\square$ (Simplify your answer.)

Answer

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Answer

So, the final answers are \(f(0,-3)=\boxed{1}\), \(f(-3,2)=\boxed{-53.875}\), and \(f(3,2)=\boxed{62}\).

Steps

Step 1 :Given the function \(f(x, y)=2^{x}+9 x y\), we are asked to find the values of \(f(0,-3)\), \(f(-3,2)\), and \(f(3,2)\).

Step 2 :To find these values, we substitute the given x and y values into the function and simplify.

Step 3 :For \(f(0,-3)\), we substitute \(x=0\) and \(y=-3\) into the function to get \(2^{0}+9*0*(-3)\), which simplifies to 1.

Step 4 :For \(f(-3,2)\), we substitute \(x=-3\) and \(y=2\) into the function to get \(2^{-3}+9*(-3)*2\), which simplifies to -53.875.

Step 5 :For \(f(3,2)\), we substitute \(x=3\) and \(y=2\) into the function to get \(2^{3}+9*3*2\), which simplifies to 62.

Step 6 :So, the final answers are \(f(0,-3)=\boxed{1}\), \(f(-3,2)=\boxed{-53.875}\), and \(f(3,2)=\boxed{62}\).

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