Answer
$$f(g(x)) = 32x^{2} - 20x + 2$$
Work Step by Step
The exercise is asking for a compound function of $f(x)$ and $g(x)$ which can also be expressed as $f(g(x))$. This means that we must substitute the entire function $g(x)$ into $f(x)$ as follows:
$$f(g(x)) = 2(4x - 1)^{2} - (4x - 1) - 1$$
which we only need to simplify. Using the "Square of a Binomial Difference" method (see page 57 for reference), we can expand $(4x - 1)^{2}$ into $(4^{2})x^{2} - 2(4)(1)x + (1) = 16x^{2} - 8x +1$ and
$$f(g(x) = 2(16x^{2} - 8x + 1) - 4x + 1 - 1$$
$$f(g(x)) = 32x^{2} - 16x + 2 - 4x$$
$$f(g(x)) = 32x^{2} - 20x + 2$$
