Answer
a. maximum $f(7)=-57$
b. domain $(-\infty,\infty)$ and range $(-\infty, -57]$
Work Step by Step
a. Given
$f(x)=-x^2+14x-106=-(x^2-14x+49)+49-106=-(x-7)^2-57$
we can find a maximum at $x=7$ with $f(7)=-57$
b. We can identify the domain as $(-\infty,\infty)$ and range as $(-\infty, -57]$
