The function f(x) varies inversely with x and f(x)=2 when x=16. what is f(x) when x=4? 128 72 40 8

The correct answer is:  [D]:  "8" .

          →   When x = 4,  f(x) = 8  .


Given the problem:


The function;  "f(x)" ; varies inversely with "x" ; and  "f(x) = 2 when x = 16 " .

What is f(x) when x = 2?


Explanation:  

Note that:  f(x) = y .

If y varies inversely with x;  then y = k/x ; with "k" being the "constant" in this equation.  

You can find the constant by substituting the values given: x = 16,  f(x) = y = 2 ;

So, f(x) = y = 2  = k/16 ; 

→  2 = k / 16 ; 

Solve for the constant; "k" ; 

Multiply EACH SIDE of the equation by "16" 

→  16* (2) = (k / 16) * 16 ;

 →  32 = k ;

  ↔  k = 32 ;  

As such, we can write the equation:
 
y = k/ x ; 

as:

→  y = 32/ x ; 

Since we are given:  "x = 4" ;  Plug in that value; and solve for "y" ;

y = 32/4 = 8 .

y = 8 .

y = f(x) ; 

So;  f(x) = 8 ;  which is:  Answer choice:  [D]:  "8" .