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Question 1074223: Hello! Thank you for your time.
I am trying to solve a function problem and so far I haven't been able to find similar practice questions where two different functions are given.
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If f(x)= 12 - (x^2 / 2) and f(2k) = 2k, what is one possible value of k?
The multiple choice options are : 2 , 3, 4, 6, 8
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What I'm stuck on: if f(2k) = 2k, wouldn't that mean 2k = 2k, thus k = k? So any value can be inputted? I'm not sure what I should do with x either...
Any insight into how to go about solving a problem like this is very much appreciated! It's been a few years since I've worked with functions. Thanks once again!
Found 3 solutions by Mini-, KMST, Edwin McCravy:
Answer by Mini-(17)   (Show Source):
You can put this solution on YOUR website! f(x) = 12 - (x^2 / 2);
If x=2k, then f(2k) = 2k;
f(2k) = 12 - ((2k)^2 / 2) = 12 - (4k^2 / 2) = 12 - 2k^2;
12 - 2k^2 = 2k;
12 = 2k^2 + 2k;
6 = k^2 + k; or k^2 + k = 6;
It is true only if k = 2, then 2^2 + 2 = 4 + 2 = 6;
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website!  is the number you get when you replace  for 
in the function (formula)  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  .
What the problem you posted says, in other words,
is to solve the equation
 ,
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:
2) SOLVING THE EQUATION:
From here, you may divide everything by 2 (or not),
and solve the equation to find the solutions are  and  .
3) THE OTHER OPTION:
 as a change of variable, tells you to solve 
 .
You could solve, you could check y=4, 6, 8, 12, and 16.
You could look at
<--> 
and decide that from the options given,
the only  that will work is  ,
because the other ones will yield too large a  .
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! If  and  ,
what is one possible value of k?
The multiple choice options are : 2 , 3, 4, 6, 8
You haven't yet gotten the concept of what f(x) and f( )
mean.
f(x) is the same thing as y, and
f( ) means the value of y when whatever is inside the
parentheses is substituted for x.
and
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In other words, yours is the same problem as this:
Given
Find a value of k such that when you substitute 2k
for x, you will get y = 2k.
So you substitute x = 2k and y = 2k
Solve that for k. You will get two solutions, and one of
them is in the list.
Try to learn to interpret functional notation.
Study that real hard until you get what it's all about:
f(x) is the same thing as y, and
f( ) means the value of y when whatever is inside the
parentheses is substituted for x.
Edwin
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