Kak, tolong di jawab yaaa no 1 sampai no 10, makasiiii.
Penjelasan dengan langkah-langkah:
f(x) = x² + 2
x + 1 = x
x = x – 1
=> (x – 1)² + 2
=> x² – 2x + 3
fog(x) = (x + 2)² + 5(x + 2) – 15
fog(x) = x² + 4x + 4 + 5x + 10 – 15
fog(x) = x² + 9x – 1
Jawab:
Penjelasan dengan langkah-langkah:
1.
f(x) = x² + 2
f(x + 1 ) = ( x + 1 )² + 2
. = x² + 2x + 1 + 2
. = x² + 2x + 3
2.
f(x) = x² + 5x – 15
g(x) = x + 2
( f o g )(x) = ( x + 2 )² + 5 ( x + 2 ) – 15
. = x² + 4x + 4 + 5x + 10 – 15
. = x² + 9x – 1
3.
f(x) = 3 – x
g(x) = x² + 2x
( fog)(x) = 3 – ( x² + 2x )
. = 3 – x² – 2x
. = -x² – 2x + 3
4.
f(x) = x² – 2x – 3
g(x) = x – 2
( fog)(x) = ( x – 2 )² – 2 ( x – 2 ) – 3
. = x² – 4x + 4 – 2x + 4 – 3
. = x² – 6x + 5
5.
f(x) = 2x² + x – 3
g(x) = x – 2
(fog)(x) = 2 ( x – 2 )² + ( x – 2 ) – 3
. = 2 ( x² – 4x + 4 ) + x – 2 – 3
. = 2x² – 8x + 8 + x – 5
. = 2x² – 7x + 3
6.
f(x) = 4x – 2
g(x) = x² + 8x + 16
( gof)(x) = ( 4x – 2 )² + 8 ( 4x – 2 ) + 16
. = 16x² – 16x + 4 + 32x – 16 + 16
. = 16x² + 16x + 4
7.
f(x) = 3x – 1
g(x) = 2x² – 3
( gof)(x) = 2 ( 3x – 1 )² – 3
. = 2 ( 9x² – 6x + 1 ) – 3
. = 18x² – 12x + 2 – 3
. = 18x² – 12x – 1
8.
f(x) = (4x – 7)/( 3 – x )
misal ;
y = (4x – 7)/( 3 – x )
y ( 3 – x ) = 4x – 7
3y – xy = 4x – 7
-xy – 4x = -3y – 7
xy + 4x = 3y + 7
x ( y + 4 ) = 3y + 7
x = ( 3y + 7)/(y + 4 )
jadi ;
f⁻¹(x) = ( 3x + 7)/(x + 4 )
9.
f(x) = 2x + 5
g(x) = ( x – 1 ) / ( x + 4 )
( fog)(x) = 2 { (x – 1 ) / ( x + 4 )} + 5
. = ( 2x – 2 )/ ( x + 4 ) + 5
. = { 2x – 2 + 5 ( x + 4 ) }/( x + 4 )
. = ( 2x – 2 + 5x + 20 )/(x + 4 )
. = ( 7x + 18 ) / ( x + 4 )
10.
( fog)(x) = 2x² + 4x + 1
f(x) = 2x – 5
f (g(x)) = 2x² + 4x + 1
2g(x) – 5 = 2x² + 4x + 1
2g(x) = 2x² + 4x + 1 + 5
2g(x) = 2x² + 4x + 6
g(x) = ( 2x² + 4x + 6 )/2
g(x) = x² + 2x + 3
semoga bisa membantu