Help me guys. tolong nomer 12 dan 13 nya pakai cara ya…..​

Jawaban:

12. A

13. A

Penjelasan dengan langkah-langkah:

12.

Pertama cari g^(-1)(x) = …

g(x) = 4x + 2

g^(-1)(4x + 2) = x

Misalkan.

(4x + 2) = a

4x = a – 2

x = (a – 2)/4

Jadi.

g^(-1)(a) = (a – 2)/4

Ubah a jadi x.

g^(-1)(x) = (x – 2)/4

Kedua, cari f^(-1)(x) = …

f(x) = x^2

f^(-1)(x^2) = x

Misalkan.

x^2 = a

x = a^(1/2)

f^(-1)(a) = a^(1/2)

Ubah a jadi x.

f^(-1)(x) = x^(1/2)

Ketiga,

(f^(-1) o g^(-1))(x) = 2

f^(-1)(g^(-1)(x)) = 2

f^(-1)((x – 2)/4) = 2

{(x-2)/4}^(1/2) = 2

penyebut 4 diakar, jadi 2, lalu dipindah ruas.

(x – 2)^(1/2) = 2 – 2

x^(1/2) – 2^(1/2) = 0

x ^(1/2) = 2^(1/2)

Kedua ruas dipangkat 2.

x = 2

13.

g^(-1)(2x/(x + 1)) = x

Misalkan.

a = 2x/(x + 1)

ax + a = 2x

2x – ax = a

x(2 – a) = a

x = a/(2-a)

g^(-1)(a) = a/(2-a)

g^(-1)(x) = x/(2 – x)

f^(-1)(x) = (x-1)/x

(f o g)^(-1)(x)

= (g^(-1) o f^(-1))(x)

= g^(-1)(f^(-1)(x))

= g^(-1)((x – 1)/x)

= {(x – 1)/x} ÷ {2 – (x + 1)/x}

= {(x – 1)/x} × {x/(x + 1)}

= (x – 1)/(x + 1) , x =/= -1