Materi : Fungsi dan Relasi

Soal Nomor 1

f(x) = x + 2

y = x + 2

x = y - 2

f-¹(x) = x - 2

g(x) = x - 5

y = x - 5

x = y + 5

g-¹(x) = x + 5

__________________________

( f-¹ o g-¹ )( x ) = f-¹( x + 5 )

= x - 2 = ( x + 5 ) - 2 = x + 3

( f-¹ o g-¹ )(2) = 2 + 3 = 5

Soal Nomor 2

f(x) = 2x²

g(x) = 4 - 2x

( f o g )( x ) = f( 4 - 2x )

= 2( 4 - 2x )²

= 2( 4x² - 16x + 16 )

= 8x² - 32x + 32

--- Invers

y = 8x² - 32x + 32

y = 8( x² - 4x + 4 )

⅛y = ( x - 2 )²

x - 2 = ± √⅛y

x = 2 ± √⅛y

( f o g )-¹(x) = 2 ± √⅛x

( f o g )-¹(2) = 2 ± ½

Himpunan Penyelesaian

x = 5/2 atau x = 3/2

Semoga bisa membantu