Question

Tolong bantu jawab, No 4e​

Answer 1

Materi : Fungsi dan Relasi

f(x) = 2x + 3

g(x) = x² - 1

h(x) = - x² + 2

__________/

( f o g o h )(x) = f(g(h(x)))

g(h(x)) = g( - x² + 2 )

= ( - x² + 2 )² - 1

= x⁴ - 4x² + 4 - 1

= x⁴ - 4x² + 3

f(g(h(x))) = f( x⁴ - 4x² + 3 )

= 2( x⁴ - 4x² + 3 ) + 3

= 2x⁴ - 8x² + 6 + 3

= 2x⁴ - 8x² + 9

( f o g o h )-¹(x)

y = 2x⁴ - 8x² + 9

y = 2( x⁴ - 4x² + 3 ) + 3

y = 2( x⁴ - 4x² + 4 - 1 ) + 3

y = 2( [ - x² + 2 ]² - 1 ) + 3

y = 2( - x² + 2 )² - 2 + 3

2( - x² + 2 )² = y - 1

( - x² + 2 )² = ( y - 1 )/2

- x² + 2 = ± √[ ( y - 1 )/2 ]

x² = 2 - ( ± √[ y - 1 )/2 ] )

x = ± √( 2 - ( ± √{ [ y - 1 ]/2 } ) )

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( f o g o h )-¹(x) = ± √( 2 - ( ± √{ [ x - 1 ]/2 } ) )

( f o g o h )-¹(1) = ± √( 2 - ( ± √{ [ 1 - 1 ]/2 } ) )

( f o g o h )-¹(1) = ± √( 2 - ( ± √(0/2) ) )

( f o g o h )-¹(1) = ± √( 2 - ( ± 0 ) )

( f o g o h )-¹(1) = ± √2

Himpunan Penyelesaian

Jika x = 1

Maka kemungkinan nilai y :

y = (+) √2 = √2

y = (-) √2 = -√2

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Semoga bisa membantu

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Answer 2

Jawaban:

(f o g o h)=f(g(h(x)))

g(h(x))

(-x²+2)²-1

=(-x²+2)(-x²+2)-1

=x⁴-4x²+4-1

=x⁴-4x²+3

.

f(x⁴-4x²+3)

2(x⁴-4x²+3)+3

=2x⁴-8x²+6+3

=2x⁴-8x²+9

.

inversikan

y=2x⁴-8x²+9

y=2(x⁴-4x²+3)+3

y=2(x⁴-4x²+4-1)+3

y=2(x²-4x²+4)-2+3

y=2((-x²+2)²)+1

y-1=2(-x²+2)²

(y-1)/2=(-x²+2)²

±√(y-1)/2=-x²+2

x²=2 - (±√(y-1)/2)

x = ± √ 2 - ( ± √ ( y - 1 ) / 2 )

y-¹= ± √ 2 - ( ± √ ( x - 1 ) / 2 )

Pada nilai x=1

± √ 2 - ( ± √ ( x - 1 ) / 2 )

± √ 2 - ( ± √ ( 1 - 1 ) / 2 )

± √ 2 - ( ± √ 0 / 2 )

± √ 2 - ( ± 0 )

± √ 2

Maka HP={ -√2 , √ 2 }

semoga bermanfaat