Dik f(x-2)=x pangkat2 +4x-7. Invers fungsi f(x) adalah.........
Matematika
ryapriansyah95
Pertanyaan
Dik f(x-2)=x pangkat2 +4x-7. Invers fungsi f(x) adalah.........
1 Jawaban
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1. Jawaban prianandalbs
f(x-2) = x² + 4x - 7
f(x-2) = (x-2)² + 8(x-2) + 5
dengan (x-2) = x , maka:
f(x) = x² + 8x + 5
y = x² + 8x + 5
x² + 8x + (5 - y) = 0
pakai rumus abc :
x1,2 = [-b +- √(b² - 4ac)]/2a
x1,2 = [-8 +- √(64 - 4(5 - y)]/2
x1,2 = [-8 +- √(44 - 4y)] / 2
x1,2 = [ -8 +- 2√(11-y)]/2
x1,2 = -4 +- √(11 - y)
adapun inversnya :
x1 = -4 + √(11 - y)
f(x) invers = -4 + √(11 - x)
x2 = -4 - √(11-y)
f(x) invers = -4 - √(11 - x)