Materi : Fungsi dan Relasi

f(x+1) = ( 2x - 7 )/( x + 1 )

(1) f(-1) = 11 { ✓ }

Nilai x untuk f(-1)

x + 1 = -1

[ x = -2 ]

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f(-1) = ( 2[-2] - 7 )/( -2 + 1 )

f(-1) = ( - 4 - 7 )/( -1 )

f(-1) = (-11)/(-1)

[ f(-1) = 11 ]

(2) f-¹(-1) = -3 [ × ]

Bentuk f-¹(x+1)

y = ( 2x + 7 )/( x + 1 )

y( x + 1 ) = 2x + 7

xy + y = 2x + 7

xy - 2x = - y + 7

x( y - 2 ) = - y + 7

x = ( - y + 7 )/( y - 2 )

f-¹(x+1) = ( - x + 7 )/( x - 2 )

Nilai x untuk f-¹(x+1) = -2

f-¹(-1) = ( - [ -2 ] + 7 )/( - 2 - 2 )

f-¹(-1) = ( 2 + 7 )/(-4)

[ f-¹(-1) = - 9/4 ]

(3) ( f o f )-¹(-1) = -9 [ × ]

Bentuk Fungsi ( f o f )(x+1)

( f o f )

= f(f(x+1))

= [ 2( { 2x - 7 }/{ x + 1 } ) - 7 ]/[ { 2x - 7 }/{ x + 1 } + 1 ]

= [ { 4x - 14 - 7x - 7 }/{ x + 1 } ]/[ { 2x - 7 + x + 1 }/{ x + 1 } ]

= { - 3x - 21 }/{ x + 1 } ÷ { 3x - 6 }/{ x + 1 }

= ( - 3x - 21 )/( 3x - 6 )

Bentuk ( f o f )-¹(x+1)

y = ( - 3x - 21 )/( 3x - 6 )

3xy - 6y = - 3x - 21

3xy + 3x = 6y - 21

x( 3y + 3 ) = 6y - 21

x = ( 6y - 21 )/( 3y + 3 )

( f o f )-¹(x+1) = ( 6x - 21 )/( 3x + 3 )

Nilai x untuk ( f o f )-¹(x+1) adalah -2

= ( 6[-2] - 21 )/( 3[-2] + 3 )

= ( - 12 - 21 )/( - 6 + 3 )

= (-33)/(-3)

[ = 11 ]

(4) 1/( f-¹[-2] ) = 4/9 [ × ]

Nilai f-¹(-2)

Nilai x untuk f-¹(-2)

x + 1 = -2

[ x = -3 ]

f-¹(-2) = ( 2[-3] - 7 )/( -3 + 1 ) = (-13)/(-2) = 13/2

Maka 1/[ f-¹(-2) ] = 1/[13/2] = 2/13

Semoga bisa membantu