Question

How do you find this?

Answer 1

g' (- 2) =
`(1)/(2)`

Explanation:

let y = g(x) and rearrange making x the subject, that is

y =
`(2)/(1-4x)` ( multiply both sides by 1 - 4x )

y(1 - 4x) = 2 ← distribute left side

y - 4xy = 2 ( subtract y from both sides )

- 4xy = 2 - y ( multiply through by - 1 )

4xy = y - 2 ( divide both sides by 4y )

x =
`(y-2)/(4y)`

change y back into terms of x with x = g'(x)

g'(x) =
`(x-2)/(4x)` , then

g'(- 2) =
`(-2-2)/(4(-2))` =
`(-4)/(-8)` =
`(1)/(2)`