Question

The function f is defined by f(x)=200÷x−b, where b is a constant. Find b, if the value of f at x= 1 3 is equal to 150.

Answer 1

`b =11 (2)/(3)`

Step-by-step explanation

The given function is

`f(x) = (200)/(x - b)`

It was given that

`f(13) = 150`

This implies that,

`150 = (200)/(13- b)`

Cross multiply to get:

`150(13 - b) = 200`

`1950 - 150b = 200`

`- 150b = 200 - 1950`

`- 150b = - 1750`

Divide both sides by -150.

`b = ( - 1750)/( - 150)`

`b = ( 35)/(3)`

`b =11 (2)/(3)`