### 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: I need to find $k$ such that $f(2) - g(2) = 2$.
I can do this by plugging in $x = 2$ into both functions and setting their difference equal to 2.
So I have $$f(2) - g(2) = 2 \implies 5(2)^2 - \frac{1}{2} + 3 - (2^2 - k) = 2$$
I can simplify this equation by expanding the brackets and combining like terms.
This gives me $$20 - \frac{1}{2} + 3 - 4 + k = 2 \implies k = -17 + \frac{1}{2}$$