Question

Diketahui f(x)=3x^2+x-7 dan g(x)=2x+1,maka tentukan:
a.(fog)(x)
b.(fog)(2)
c.(gof)(x)
d.(gof)(2x+3)
petunjuk:^=pangkat
o=bundaran

Answer 1

A. (fog)(x)
= f(g(x))
= 3(2x + 1)² + (2x + 1) - 7
= 3(4x² + 4x + 1) + 2x + 1 - 7
= 12x² + 12x + 3 + 2x + 1 - 7
= 12x² + 14x - 3

b. (fog)(2)
= 12(2)² + 14(2) - 3
= 12(4) + 28 - 3
= 48 + 28 - 3
= 73

c. (gof)(x)
= g(f(x))
= 2(3x² + x - 7) + 1
= 6x² + 2x - 14 + 1
= 6x² + 2x - 13

d. (gof)(2x + 3)
= 6(2x + 3)² + 2(2x + 3) - 13
= 6(4x² + 12x + 9) + 4x + 6 - 13
= 24x² + 72x + 54 + 4x + 6 - 13
= 24x² + 76x + 47