Question

f(2x-1)=4x^2+6x求f(X^2+2)

写清楚一点了

Answer 1

令 2x-1 =y 则：x = (y+1)/2
f(y) = f(2x-1) = 4x^2 + 6x = y^2 +2y+1+3y+3 = y^2 +5y+4 即：f(y)=(y+1)*(y+4)
f(x^2+2)=(x^2+2+1)*(x^2+2+4) = (x^2+3)*(x^2+6) = x^4+9x^2+18

Answer 2

令2x-1=t,则
f(t)=4(2t-1)^2+6(2t-1)
=16t^2-4t-2

所以f(x^2+2)
=16(x^2+2)^2-4(x^2+2)-2
=16x^4+60x^2+54

Answer 3

令t=2x-1,得x=(t+1)/2带入得f(t)=t^2+5t+4
所以f(X^2+2)=(X^2+2)^2+5(X^2+2)+4=x^4+9x^2+18

Answer 4

令t=2x-1,则x=(t+1)/2;
f(2x-1)=f(t)=(t+1)^+3(t+1)=t^+5t+1;
f(x)=x^+5x+1;
f(x^+2)=(x^+2)^+5(x^+2)+1=x(4次方)+9x^+15

Answer 5

设2x-1=t
x=(t+1)/2
f(t)=4*[(t+1)/2]^2+6(t+1)/2

f(x^2+2)
=4*[(x^2+2+1)/2]^2+6*(x^2+2+1)/2
=x^4+9*x^2+18