Diketahui fungsi f(x)=3x-7 dan g(x)=x2-3,tentukan

Jawaban:

a. fog (x) = 3x² – 16

b. gof (x) = 9x² – 42x + 46

c. fog (3) = 11

d. gof (5) = 22

Penjelasan dengan langkah-langkah:

a. fog (x) = f (g(x))

= f (x²-3)

f (x) = 3x-7

= 3 (x²-3) – 7

= 3x² – 9 – 7

= 3x² – 16

b. gof (x) = g (f(x))

= g (3x-7)

g (x) = x² – 3

= (3x-7)² – 3

= (3x – 7) (3x – 7) – 3

= 9x²- 21x – 21x + 49 – 3

= 9x² – 42x + 46

c. fog (3) = f (g(3))

= f (3² – 3)

= f (9 – 3)

= f (6)

f (x) = 3x – 7

= 3 (6) – 7

= 18 – 7

= 11

d. gof (5) = g (f(5))

= g (3x-7)

= g (3(5) – 7)

= g (35 – 7)

= g (28)

g (x) = x² – 3

= (5)² – 3

= 25 – 3

= 22