Penjelasan dengan langkah-langkah:

Fungsi Relasi

f(x) = x² + 2x - 6

a). nilai f(x), jika x = 0

f(x) = x² + 2x - 6

f(0) = 0² + 2(0) - 6

f(0) = 0+0-6

f(0) = -6

b). nilai a , jika f(a) = 0

x² + 2x - 6 = f(x)

a² + 2a - 6 = f(a)

a² + 2a - 6 = 0

a = 1 , b = 2 , c = -6

D = b²-4ac = 2² - 4(1)(-6)= 4+24 = 28

.

a1,2 = (-b ± √D)/2a

a1,2 = (-2 ± √28)/2(1)

a1,2 = (-2 ± 2√7)/2

solusi:

a1 = (-2+2√7)/2 = -1+√7

a2 = (-2-2√7)/2 = -1-√7

HP = { -1 ± √7 }

d). nilai n, jika f(n) = 2

x² + 2x - 6 = f(x)

n² + 2n - 6 = f(n)

n² + 2n - 6 = 2

n² + 2n - 6-2 = 0

n² + 2n - 8 = 0

n² + 4n - 2n - 8 = 0

n(n + 4) - 2(n + 4) = 0

(n - 2)(n + 4) = 0

Solusi:

n1 = 2 atau n2 = -4

HP = { -4 , 2 }