Question

If f(x) varies directly with x and f(x) = 40 when x = 8, find the value of f(x) when x = 2.

Answer 1

For this case we have a function of the form:

`f (x) = kx`

We must find the constant of proportionality. For this, we use the following data:

`f (x) = 40\ and\ x = 8`

Substituting values we have:

`40 = k * 8`

Clearing k we have:

`k = \frac {40} {8}\\k = 5`

Therefore, the function is given by:

`f (x) = 5x`

For
`x = 2` we have:

`f (2) = 5 * 2\\f (2) = 10`

Answer:

the value of the function for
`x = 2` is:
`f (2) = 10`

Answer 2

f(x) = 10

Explanation:

for direct variation

f(x) = kx

substitute in for f(x) and x

40 = k*8

solve for k

40/8 = k*8/8

5 =k

now we have

f(x) = 5*x

let x=2

f(x) = 5*2

f(x) = 10