Jawab:
fungsi komposisi
gof (x) = g { f(x) }
Penjelasan dengan langkah-langkah:
g(x) = 4x² + 6x - 3
misal f(x) = ax+ b
gof(x) = x² +7x + 7
g{ax+ b } = x² +7x + 7
4 (ax+ b)² +6 (ax + b) - 3 = x² + 7x + 7
4 (a² x² + 2 ab x + b²) + 6 ax + 6b - 3 = x² +7x + 7
4a² x² + 8 ab x + 4b² + 6a x + 6 b - 3 = x² +7x + 7
4a² x² + (8ab + 6a) x + (4v² +6b -3) = x² +7x + 7
4a² = 1 --> a²= 1/4 --> a= 1/2
8 ab + 6a = 7
8(1/2) b + 6(1/2) = 7
4b + 3 = 7
4b = 4
b = 1
f(x)= ax + b = 1/2 x + 1
f(2a - 4) = 1/2 (2a- 4) + 1
f(2a- 4) = a - 2 + 1
f(2a - 4) = a - 1
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Verified answer
Jawab:
fungsi komposisi
gof (x) = g { f(x) }
Penjelasan dengan langkah-langkah:
g(x) = 4x² + 6x - 3
misal f(x) = ax+ b
gof(x) = x² +7x + 7
g{ax+ b } = x² +7x + 7
4 (ax+ b)² +6 (ax + b) - 3 = x² + 7x + 7
4 (a² x² + 2 ab x + b²) + 6 ax + 6b - 3 = x² +7x + 7
4a² x² + 8 ab x + 4b² + 6a x + 6 b - 3 = x² +7x + 7
4a² x² + (8ab + 6a) x + (4v² +6b -3) = x² +7x + 7
4a² = 1 --> a²= 1/4 --> a= 1/2
8 ab + 6a = 7
8(1/2) b + 6(1/2) = 7
4b + 3 = 7
4b = 4
b = 1
f(x)= ax + b = 1/2 x + 1
f(2a - 4) = 1/2 (2a- 4) + 1
f(2a- 4) = a - 2 + 1
f(2a - 4) = a - 1