F(x) = ax + b f(f(x)) = a f(x) + b 4x + 12 = a(ax + b) + b 4x + 12 = a^2 x + ab + b 4x + 12 = a^2 x + (ab + b) Koefisien x a^2 = 4 => a = ± 2 => a = 2 atau a = -2
Konstanta ab + b = 12 a = 2 => 2b + b = 12 => 3b = 12 => b = 4 (memenuhi karena a < b) a = -2 => -2b + b = 12 => -b = 12 => b = -12 (tidak memenuhi krn a > b)
Jadi a = 2 dan b = 4 f(x) = ax + b = 2x + 4 f(-1) = 2(-1) + 4 = 2
Verified answer
F(x) = ax + bf(f(x)) = a f(x) + b
4x + 12 = a(ax + b) + b
4x + 12 = a^2 x + ab + b
4x + 12 = a^2 x + (ab + b)
Koefisien x
a^2 = 4 => a = ± 2 => a = 2 atau a = -2
Konstanta
ab + b = 12
a = 2 => 2b + b = 12 => 3b = 12 => b = 4 (memenuhi karena a < b)
a = -2 => -2b + b = 12 => -b = 12 => b = -12 (tidak memenuhi krn a > b)
Jadi a = 2 dan b = 4
f(x) = ax + b = 2x + 4
f(-1) = 2(-1) + 4 = 2