Answer:
g' (- 2) = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
let y = g(x) and rearrange making x the subject, that is
y = [tex]\frac{2}{1-4x}[/tex] ( 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 = [tex]\frac{y-2}{4y}[/tex]
change y back into terms of x with x = g'(x)
g'(x) = [tex]\frac{x-2}{4x}[/tex] , then
g'(- 2) = [tex]\frac{-2-2}{4(-2)}[/tex] = [tex]\frac{-4}{-8}[/tex] = [tex]\frac{1}{2}[/tex]
