di ketahui fungsi f di definisikan sebagai f(x)=2x²+3x+1 tentukan nilai fungsi f(x) untuk: a.f(x+2) b.f(3x) c.f(5) d.f(x-3)

jwb

f(x) = 2x² + 3x + 1

f(x+2) = 2(x+2)² + 3(x +2) + 1
= 2(x²+4x+4) + 3x +6 +1
= 2x²+8x+8 +3x +6+1
= 2x²+ 11x + 15

f(3x) = 2(3x)² + 3(3x) + 1
= 2(9x²) + 9x +1
= 18x² +9x + 1

f(5) = 2(5)² + 3(5)+ 1
= 2(25)+ 15 + 1 = 50 + 15 +1
= 66

f(x-3) = 2 (x-3)² + 3(x-3) + 1
= 3(x²-6x +9) + 3x  - 9 + 1
= 3x² -18x + 27 + 3x -9 +1
= 3x² - 15x + 19

f(x) = 2x² + 3x + 1 = (2x + 1)(x + 1)

•
f(x + 2)
= (2(x + 2) + 1)(x + 2 + 1)
= (2x + 5)(x + 3)

••
f(3x)
= (2(3x) + 1)(3x + 1)
= (6x + 1)(3x + 1)

•••
f(5)
= (2.5 + 1)(5 + 1)
= 11 × 6
= 66

••••
f(x - 3)
= (2(x - 3) + 1)(x - 3 + 1)
= (2x - 5)(x - 2)