b) invers dari 2x + 5/ 2x -2 y = 2x + 5/ 2x -2 2xy - 2y = 2x + 5 2xy - 2x = 5 + 2y x(2y - 2) = 5 + 2y x = 5 + 2y / 2y - 2 Maka invers nya adalah (5 + 2x) / (2x - 2)
2. a) g o f = g (f(x)) = 11 (8x + 2 / 3 - 5x) + 20 g o f = 88x + 22 / (3 - 5x) + 20 samain penyebut g o f = 88x + 22 + 60 - 100x / (3 - 5x)\ g o f = (-12x + 82) / (3 - 5x)
b) invers dari g o f y = -12x + 82 / 3 - 5x 3y - 5xy = -12x + 82 12x - 5xy = -3y + 82 x(12 - 5y) = -3y + 82 x = -3y + 82/ (12 - 5y) Maka invers g o f = (-3x + 82)/ (12 - 5x)
f(x) = 2x + 3
g(x) = ( x + 2 ) / ( x - 5 )
(a) ( g o f )(x) = g [ f(x) ]
= g ( 2x + 3 )
= ( 2x + 3 + 2 ) / ( 2x + 3 - 5 )
= ( 2x + 5 ) / ( 2x - 2 )
(b) Rumus :
y = ( ax + b ) / ( cx + d ) ---> y⁻¹ = ( -dx + b ) / ( cx - a )
( g o f )(x) = ( 2x + 5 ) / ( 2x - 2 )
( g o f )⁻¹ (x) = ( 2x + 5 ) / ( 2x - 2 ) ---> invers ( g o f )(x) tidak berubah
No. [2] :
f(x) = ( 8x + 2 ) / ( 3 - 5x )
g(x) = 11x + 20
(a) ( g o f )(x) = g [ f(x) ]
= g [ ( 8x + 2 ) / ( 3 - 5x ) ]
= 11 [ ( 8x + 2 ) / ( 3 - 5x ) ] + 20
= [ ( 88x + 22 ) / ( 3 - 5x ) ] + 20 ---> samakan penyebut
= [ ( 88x + 22 ) / ( 3 - 5x ) ] + [ 20 ( 3 - 5x ) / ( 3 - 5x ) ]
= [ ( 88x + 22 ) / ( 3 - 5x ) ] + [ ( 60 - 100x ) / ( 3 - 5x ) ]
= [ ( 88x + 22 ) + ( 60 - 100x ) ] / ( 3 - 5x )
= ( -12x + 82 ) / ( -5x + 3 )
(b) Rumus :
y = ( ax + b ) / ( cx + d ) ---> y⁻¹ = ( -dx + b ) / ( cx - a )
( g o f )(x) = ( -12x + 82 ) / ( -5x + 3 )
( g o f )⁻¹ (x) = ( -3x + 5 ) / ( -5x + 12 )
b) invers dari 2x + 5/ 2x -2
y = 2x + 5/ 2x -2
2xy - 2y = 2x + 5
2xy - 2x = 5 + 2y
x(2y - 2) = 5 + 2y
x = 5 + 2y / 2y - 2
Maka invers nya adalah (5 + 2x) / (2x - 2)
2. a) g o f = g (f(x)) = 11 (8x + 2 / 3 - 5x) + 20
g o f = 88x + 22 / (3 - 5x) + 20
samain penyebut
g o f = 88x + 22 + 60 - 100x / (3 - 5x)\
g o f = (-12x + 82) / (3 - 5x)
b) invers dari g o f
y = -12x + 82 / 3 - 5x
3y - 5xy = -12x + 82
12x - 5xy = -3y + 82
x(12 - 5y) = -3y + 82
x = -3y + 82/ (12 - 5y)
Maka invers g o f = (-3x + 82)/ (12 - 5x)
Semoga Membantu ^^