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" .

To subtract integers, change the sign on the integer that is to be subtracted. If both signs are positive, the answer will be positive. If both signs are negative, the answer will be negative. If the signs are different subtract the smaller absolute value from the larger absolute value.

Step-by-step explanation: