Answer
$$f(g(x)) = 2x^{2} -3x + 2$$
$$and$$
$$g(f(x)) = 2x^{2} - x - 2$$
Work Step by Step
The exercise in question is basically asking us to find $f(g(x))$ and $g(f(x))$. Knowing that $g(x) = 1 - x$, and that $f(x) = 2x^{2} - x -1$, to find $f(g(x))$ we simply substitute $g(x)$ inside the values of $x$ from $f(x)$ as so:
$f(g(x)) = 2[x - 1]^{2} - [x - 1] - 1$
$f(g(x)) = 2[x^{2} - 2x +1] - x + 1 - 1$
$f(g(x)) = 2x^{2} - 4x +2 - x$
$f(g(x)) = 2x^{2} -3x + 2$
Following the same principles, we can find the following:
$g(f(x)) = [2x^{2} - x - 1] - 1$
$g(f(x)) = 2x^{2} - x - 1 - 1$
$g(f(x)) = 2x^{2} - x - 2$
