Respuesta :

Answer:

72

Step-by-step explanation:

Given that f(x) varies directly with x the the equation relating them is

f(x) = kx ← k is the constant of variation

To find k use the condition f(x) = 24 when x = 2

k = [tex]\frac{f(x)}{x}[/tex] = [tex]\frac{24}{2}[/tex] = 12

f(x) = 12x ← equation of variation

When x = 6, then

f(6) = 12 × 6 = 72

ajeigbeibraheem

The value of f(x) is 72.

We are being told that;

Suppose f(x) ∝ x; i.e. f(x) = kx

  • where (k) is constant

Then;

f(x) = x

∴

when f(x) is 24  ,   x = 2

We are to determine what f(x) will be when x = 6. Equating the two expressions as a system of linear terms, we have:

  • 24 = 2
  • f(x) = 6

By cross multiplying the two terms, we have;

24  × 6 = 2 × f(x)

144 = 2f(x)

f(x) = 144/2

f(x) = 72

Learn more about direct variation here:

https://brainly.com/question/13977805?referrer=searchResults

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