Question

Suppose f(x) varies directly with x and f(x)=24 when x = 2. What is the value of f(x) when x = 6? responses 48 48 112 1 over 12 12 1 half 72 72

Answer 1

The value of f(x) when x = 6 is 72, found by determining the constant of proportionality in the direct variation equation and then substituting x with 6.

Step-by-step explanation:

Since f(x) varies directly with x, we can express this relationship as f(x) = kx where k is the constant of proportionality. With f(2) = 24, we can find k as follows: f(2) = k × 2 = 24, leading to k = 12.

Now, to find f(x) when x = 6, we substitute x with 6 into the direct variation formula: f(x) = kx, giving us f(6) = 12 × 6 = 72.

Therefore, the value of f(x) when x = 6 is 72.