Tentukan nilai (gof)-1(2) jika f(×)=5x+2 dan g(x)=3x-1​

• Fungsi Kompoisis – InveRS

–

f(x) = 5x + 2

g(x) = 3x – 1

{g o f}⁻¹{2} = … ?

•••

{g o f}{x} = g{f{x}}

{g o f}{x} = 3{5x + 2} – 1

{g o f}{x} = 15x + 6 – 1

{g o f}{x} = 15x + 5

           y = 15x + 5

       15x = y – 5

           x = {y – 5} / 15

Maka :

{g o f}⁻{x} = {x – 5} / 15

{g o f}⁻¹{2} = {2 – 5} / 15

{g o f}⁻¹{2} = -3/15

{g o f}⁻¹{2} = -1/5

•••

Jawaban:

• Invers

————

f(x) = 5x + 2

g(x) = 3x – 1

Maka,

gof(x)

= g(f(x))

= g(5x + 2)

= 3(5x + 2) – 1

= 15x + 6 – 1

= 15x + 5

Invers

y = 15x + 5

y – 5 = 15x

x = (y – 5) / 15

Maka,

gof^-1(x) = (x – 5) / 15

gof^-1(2) = (2 – 5) / 15

= -3 / 15

= -1 / 5