[tex]f(x) = \frac{3x + 4}{2x + 5} \\ gof(x) = 4x + 5[/tex] tentukan [tex]g(x) = [/tex]

jawab

f(x) = (3x + 4)/(2x + 5)
y  = (3x + 4)/ (2x + 5)
3x+ 4 = y(2x + 5)
3x - 2xy = 5y - 4
x( 3 - 2y) = (5y - 4)
x =  (5y - 4)/(3 - 2y)
f⁻⁻¹ (x) = (5x - 4)/(3 - 2x)

gof(x) = 4x + 5
g(x) = (gof) o f⁻⁻¹
g(x) =  4 .f⁻¹ + 5
g(x) = 4(5x - 4)/(3 -2x)  + 5

g(x) = [ 4(5x-4) + 5(3 - 2x)] / (3 -2x)

g(x) = [ 20x -16 + 15 -10x ] / (3 -2x)

g(x) = [ 10x - 1 ] / [ 3 - 2x ]