Mohon dibantu kak:)Hari ini dikumpulin​

penjelasan:

f(x) = 2x – 1

g(x) = frac{x + 3}{2 – x}

2−x

x+3

(f o g)(x) = f(g(x))

(f o g)(x) = 2 g(x) – 1

(f o g)(x) = 2 left(frac{x + 3}{2 – x}right) – 12(

2−x

x+3

)−1

(f o g)(x) = frac{2x + 6}{2 – x} – frac{2 – x}{2 – x}

2−x

2x+6

−

2−x

2−x

(f o g)(x) = frac{2x + 6 – 2 + x}{2 – x}

2−x

2x+6−2+x

(f o g)(x) = frac{3x + 4}{2 – x}

2−x

3x+4

Misal

(f o g)(x) = y

frac{3x + 4}{2 – x}

2−x

3x+4

= y

3x + 4 = y(2 – x)

3x + 4 = 2y – yx

yx + 3x = 2y – 4

x(y + 3) = 2y – 4

x = frac{2y – 4}{y + 3}

y+3

2y−4

(f o g)⁻¹ (x) = frac{2x – 4}{x + 3}

x+3

2x−4

Cara lain

f(x) = frac{ax + b}{cx + d}

cx+d

ax+b

maka

f⁻¹ (x) = frac{-dx + b}{cx – a}

cx−a

−dx+b

Jadi jika

(f o g)(x) = frac{3x + 4}{2 – x}

2−x

3x+4

(f o g)(x) = frac{3x + 4}{-x + 2}

−x+2

3x+4

maka

(f o g)⁻¹ (x) = frac{-2x + 4}{-x – 3}

−x−3

−2x+4

(f o g)⁻¹ (x) = frac{-(2x – 4)}{-(x + 3)}

−(x+3)

−(2x−4)

(f o g)⁻¹ (x) = frac{2x – 4}{x + 3}

x+3

2x−4