#matematika wajib kls10

Fungsi
Kelas X

[tex] f(x) = \frac{1}{\sqrt{x^2 - 8x +12}} \\
\\
a. \ Terdefinisi \ jika \ penyebut \ lebih \\ besar \ dari \ 0 [/tex]
√(x² - 8x + 12) > 0
x² - 8x + 12 > 0
(x - 6)(x - 2) > 0
x < 2 atau x > 6

Domain : {x | x < 2 atau x > 6 , x ∈ R}

[tex] b. \ f(-3) = \frac{1}{\sqrt{(-3)^2 - 8(-3) + 12}} \\
= \frac{1}{\sqrt{45}} \\
= \frac{\sqrt{45}}{45} [/tex]

[tex] c. \ \frac15 \sqrt5 = \frac{1}{\sqrt5} \\
f(a) = \frac{1}{\sqrt{a^2 - 8a +12}} \\
\frac{1}{\sqrt{a^2 - 8a +12}} = \frac{1}{\sqrt5} [/tex]
√5 = √(a² - 8a + 12)
5 = a² - 8a + 12
a² - 8a + 7 = 0
(a - 7)(a - 1) = 0
a = 7 atau a = 1