#### Answer

not one-to-one

#### Work Step by Step

When we see $($... x ...$)^{2}$ in the function expression,
our first thought should be
"this is probably not one-to-one",
because, for example, $1^{2}=(-1)^{2}=1$...
We can get 1 in the parentheses if $x=7$
and $-1$ if $x=5. $
So, for two different values from the domain, $-7$ and $5$...
$f(-7)=-3(1)^{2}+8=5$
$f(5)=-3(-1)^{2}+8=5$
... we have the same function value.