Question

How do you find this?

Answer 1

Answer:

g' (- 2) = $\frac{1}{2}$

Step-by-step explanation:

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

y = $\frac{2}{1-4x}$ ( 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 = $\frac{y-2}{4y}$

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

g'(x) = $\frac{x-2}{4x}$ , then

g'(- 2) = $\frac{-2-2}{4(-2)}$ = $\frac{-4}{-8}$ = $\frac{1}{2}$