diketahui f(2x-1)=8x²+x+5 dan g(4x+1/3)=7x-1 tentukan f(x) dan g(x)

jawab

f(2x -1)= 8x² + x  + 5
2x- 1 = y
x = 1/2 (y+1)
f(y) = 8{ 1/2 (y+1)}² + 1/2(y + 1)  + 5
f(x) = 8 { 1/2 (x+1)}²+1/2 (x + 1) + 5
f(x) = 8 {1/4 (x²+2x + 1)} + 1/2 x + 1/2 + 5
f(x) = 2 (x² + 2x + 1) + 1/2 x + 1/2 + 5
f(x )= 2x² + 4x + 2 + 1/2 x + 1/2 + 5
f(x) = 2x² + 4 1/2 x + 7 1/2
f(x) = 1/2 (4x² + 9 x + 15)

g{(4x + 1)/3} = 7x - 1
(4x+ 1)/3 = y
4x+ 1 = 3y
4x = 3y - 1
x = 1/4 ( 3y - 1)

g(y)= 7 { 1/4 (3y -1)}
g(x) = 7 { 1/4 (3x - 1)}
g(x) = 7/4 (3x + 1)
atau
g(x ) = 1/4 (21 x + 7)
atau
g(x) = (21x + 7) /4

g((4x+1)/3) = 7x - 1

y = (4x+1)/3
3y = 4x + 1
4x = 3y - 1
x = (3y - 1) / 4

g(y) = 7((3y - 1) / 4) - 1
g(x) = 7((3x - 1) / 4) - 1
g(x) = (21x - 7)/4  - 4/4
g(x) = (21x - 11)/4
g(x) = (1/4) (21x - 7)