4題涵數(難)

已知H(x)=5(x+1)(x-2),G(x )=8-3x,求下列各題的表達式
1.G[H(t)]
=8-3[H(t)]
=8-3[5(t+1)(t-2)]
=8-15(t^2-t-2)
=8-15t^2+15t+30
=-15t^2+15t+38

2) 2H[G(t)]
=2{5([G(t)]+1)([G(t)]-2)}
=10(8-3t+1)(8-3t-2)
=10(9-3t)(6-3t)
=10(54-27t-18t+9t^2)
=90t^2-450t+540

已知f(x)=6-5x^2 , g(x)=2X^2+X-3,求下列各題的表達式
3) g[f(w)]+3
=2(6-5w^2)^2+6-5w^2-3+3
=2(36-60w^2+25w^4)+6-5w^2
=50w^4-120w^2-5w^2+72+6
=50w^4-125w^2+78

4) 4w-f[g(w)]
=4w-[6-5(2w^2+w-3)^2]
=4w-{6-5[4w^4+4w^3+w^2-6(2w^2+w)+9]}
=4w-[6-5(4w^4+4w^3+w^2-12w^2-6w+9)]
=4w-[6-20w^4-20w^3-5w^2+60w^2+30w-45]
=20w^4+20w^3-55w^2-26w+39