Berikut ini adalah pertanyaan dari buried6feetunder pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas
Jawaban dan Penjelasan
Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.
1. f(x) = x²
g(x) = 3x
h(x) = 3x² + 1
a) ( h o g o f )(x) = h o g [ f(x) ]
= h o g(x²)
= h [ 3(x²) ]
= h(3x²)
= 3(3x²) + 1
= 9x² + 1
( f o g o h )(x) = f o g [ h(x) ]
= f o g( 3x² + 1 )
= f [ 3( 3x² + 1 ) ]
= f( 9x² + 3 )
= ( 9x² + 3 )²
= 81x⁴ + 27x² + 27x² + 9
= 81x⁴ + 54x² + 9
b) ( g o h o f )(x) = g o h [ f(x) ]
= g o h(x²)
= g [ 3(x²)² + 1 ]
= g( 3x⁴ + 1 )
= 3( 3x⁴ + 1 )
= 9x⁴ + 3
( g o h o f )(-2) = 9(-2)⁴ + 3
= 9.16 + 3
= 144 + 3 = 147
( g o f o h )(x) = g o f [ h(x) ]
= g o f( 3x² + 1 )
= g [ ( 3x² + 1 )² ]
= g( 9x⁴ + 6x² + 1 )
= 3( 9x⁴ + 6x² + 1 )
= 27x⁴ + 18x² + 3
( g o f o h )(-2) = 27(-2)⁴ + 18(-2)² + 3
= 27.16 + 18.4 + 3
= 432 + 72 + 3
= 507
2. f(x) = 2x - 1
g(x) = 3x
h(x) = x² + 1
a) ( f o h o g )(x) = f o h [ g(x) ]
= f o h(3x)
= f [ (3x)² + 1 ]
= f( 9x² + 1 )
= 2( 9x² + 1 ) - 1
= 18x² + 2 - 1
= 18x² + 1
( f o h o g )(2) = 18.2² + 1
= 18.4 + 1
= 72 + 1 = 73
( h o g o f )(x) = h o g [ f(x) ]
= h o g( 2x - 1 )
= h [ 3( 2x - 1 ) ]
= h( 6x - 3 )
= ( 6x - 3 )² + 1
= 36x² - 36x + 9 + 1
= 36x² - 36x + 10
( h o g o f )(2) = 36.2² - 36.2 + 10
= 36.4 - 72 + 10
= 144 - 62 = 82
b) ( h o g o f )( x-1 )
= 36( x + 1 )² - 36( x + 1 ) + 10
= 36( x² + 2x + 1 ) - 36x - 36 + 10
= 36x² + 72x + 36 - 36x - 26
= 36x² + 36x +10
( f o g o h )(x) = f o g [ h(x) ]
= f o g( x² + 1 )
= f [ 3( x² + 1 ) ]
= f( 3x² + 3 )
= 2( 3x² + 3 ) - 1
= 6x² + 6 - 1
= 6x² + 5
( f o g o h )( x - 1 ) = 6( x - 1 )² + 5
= 6( x² - 2x + 1 ) + 5
= 6x² - 12x + 6 + 5
= 6x² - 12x + 11
3. a) f(x) = y
3x - 2 = y
3x = y + 2
g(x) = y
5x + 2 = y( 3x - 2 )
5x + 2 = 3yx - 2y
5x - 3yx = -2y - 2
( 5 - 3y ) x = -2y - 2
b) ( f⁻¹ o g⁻¹ ) = f⁻¹ [ g⁻¹(x) ]
( g o f )(x) = g [ f(x) ]
= g( 3x - 2 )
( g o f )(x) = y
15x - 8 = y( 9x - 8 )
15x - 8 = 9yx - 8y
15x - 9yx = -8x + 8
( 15 - 9y ) x = -8x + 8
4. ( g o f )(x) = g [ f(x) ]
4x² + 8x - 3 = g( 2x + 4 )
Misal : 2x + 4 = R
2x = R - 4
x = ( R - 4 )/2
4[ ( R - 4 )/2 ]² + 8[ ( R - 4 )/2 ] - 3 = g(R)
4[ ( R² - 8R + 16 )/4 ] + 4( R - 4 ) - 3 = g(R)
R² - 8R + 16 + 4R - 16 - 3 = g(R)
R² - 4R - 3 = g(R)
g(x) = x² - 4x - 3
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Last Update: Sat, 07 May 22