invers fungsi f(x) = (2x - 3) ÷ (4x + 1) g(x) = x - 2 nilai (f o g)invers (x) adalah...

jawab

f(x)= (2x - 3)/(4x +1)
y = (2x -3)/ (4x + 1)
y(4x +1) = 2x - 3
4xy + y = 2x - 3
4xy - 2x = -y-3
x(4y -2) = (-y - 3)
x = (-y - 3)/(4y - 2)
f⁻¹(x) = (-x-3)/(4x - 2) 
atau
f⁻¹(x) = (x +3)/(2 - 4x)

g(x) = x - 2
y = x -2
x = y + 2
g⁻¹(x) = x + 2

(fog)⁻¹(x) = g⁻¹ o f⁻¹ (x)
= g⁻¹ { f⁻¹(x)}
= g⁻¹ {(x+3) /(2-4x)}
=  (x+3)/(2 -4x) + 2

= { x + 3 + 2(2 -4x)} / (2 - 4x)
= ( x + 3 + 4 - 8x )/ (2 - 4x)
= (7 - 7x)/(2 - 4x)