### Instruction: Consider the given functions: $$\begin{array}{ccc}
f(x) & = & 5x^2 - \frac{1}{x}+ 3\\
g(x) & = & x^2-k
\end{array}$$If $f(2) - g(2) = 2$, what is the value of $k$?### Response: To find $k$, I need to plug in $x=2$ into both functions and see what they equal.
For $f(2)$, I get $5(2)^2 - \frac{1}{2} + 3 = 20 - \frac{1}{2} + 3 = 22.5$.
For $g(2)$, I get $(2)^2 - k = 4 - k$.
Now I can set up an equation using the given information: $f(2) - g(2) = 2$.
Substituting the values I found, I get $22.5 - (4 - k) = 2$.
Simplifying, I get $18.5 + k = 2$, so $k = -16.5$.