Given $f(x) = 2x^2 − 3$:

1. Evaluate $f(2)$.

   Hint (a):

   Substitute $2$ in for every $x$ in the equation.

   $2(2^²) − 3$

   Answer (a):

   $f(2) = 5$

2. Without writing the equation of the inverse, determine $f ^{-1}(5)$. Explain your process.

   Hint (b):

   Recall that that the inputs and outputs are switched for the inverse of a function.

   More Help (b):

   What was the result you found in part (a)? How can you use that to find $f ^{-1}(5)$?

3. Solve for $x$ if $f(x + 2) - f(x - 2) = 64$.

   Hint 1(c):

   $f(x + 2) = 2((x + 2)^²) - 3 f(x − 2) = 2((x − 2)^²) - 3$

   Hint 2(c):

   Substitute these formulas into the equation above. $[2((x + 2)^2) − 3] − [2((x − 2)^2) − 3] = 64$

   Hint 3(c):

   Solve for $x$.