Question 1074223
{{{f(2k)}}} is the number you get when you replace {{{2k}}} for {{{x}}}
in the function (formula) {{{f(x)="..."}}} given.
 

The unexpected brackets add no meaning, but they do not hurt.
They are unexpected because "f(x)= 12 - (x^2 / 2) ".
means the same as f(x) = 12 - x^2 /2 , or {{{f(x) = 12 - x^2 /2}}} .
 
What the problem you posted says, in other words,
is to solve the equation
{{{12-((2k)^2/2)=2k}}} ,
or at least verify if one of the solutions given makes the equation true.
 
This looks like a problem you may face in a timed test,
so finding the most effective strategy will help.
(I failed at strategy this time, but hindsight may help me next time).
 
1) CHECKING THE CHOICES:
{{{matrix(4,6,"k =",2,3,4,6,8,
"2 k =",4,6,8,12,16,
"f ( 2 k ) =",12-4^2/2=12-16/2=12-8,12-6^2/2,negative,negative,negative,
" ","=4","=12-36/2=12-18=-6",number,number,number)}}}
 
2) SOLVING THE EQUATION:
{{{12-(2k)^2/2=2k}}}
{{{12-4k^2/2=2k}}}
{{{12-2k^2=2k}}}
From here, you may divide everything by 2 (or not),
and solve the equation to find the solutions are {{{k=2}}} and {{{k=-3}}} .
 
3) THE OTHER OPTION:
{{{y=2k}}} as a change of variable, tells you to solve {{{f(y)=y}}}
{{{12-y^2/2=y}}} .
You could solve, you could check y=4, 6, 8, 12, and 16.
You could look at
{{{12-y^2/2=y}}} <--> {{{12-y=y^2/2}}}
and decide that from the options given,
the only {{{y^2/2}}} that will work is {{{4^2/2=16/2=8}}} ,
because the other ones will yield too large a {{{y^2/2>=6^2/2=36/2=18}}} .