Question

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

What is f(x) when x = 4?

Answer 1

Answer: The correct answer is: [D]: "8" .

Step-by-step explanation:f 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" .