Question

用matlab编程求出y=-0.0855*x^3+0.0245*x^2+0.4983*x+0.4855 的的反函数，并y等于（0，1）的随机数时x的值

Answer 1

>> syms x y
>> x=solve('y=-0.0855*x^3+0.0245*x^2+0.4983*x+0.4855')

x =

1.9518134734714195060968427132375/(((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3) + (((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3) + 0.09551656920077972709551656920078
0.09551656920077972709551656920078 + (((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3)*(- 0.86602540378443864676372317075294*i - 0.5) + (1.6903200514749938066147015794976*i - 0.97590673673570975304842135661875)/(((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3)
0.09551656920077972709551656920078 + (((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3)*(0.86602540378443864676372317075294*i - 0.5) + (- 1.6903200514749938066147015794976*i - 0.97590673673570975304842135661875)/(((5.8479532163742690058479532163743*y - 3.1183913579587682140554409344666)^2 - 7.4355814434024474123676612805896)^(1/2) - 5.8479532163742690058479532163743*y + 3.1183913579587682140554409344666)^(1/3)

>> y=rand(1)

y =

0.8147

>> subs(x)

ans =

2.1596 - 0.0000i
0.6944 + 0.0000i
-2.5675 - 0.0000i

个人建议，先对原函数拟合，再就反函数。如何？？？？？？？
用matlab工具箱进行拟合，可以得到，用指数函数拟合的结果：

General model Power2:
f(x) = a*x^b+c
Coefficients (with 95% confidence bounds):
a = -0.0833 (-0.08339, -0.08321)
b = 3.005 (3.005, 3.005)
c = 11.88 (10.34, 13.42)

Goodness of fit:
SSE: 1829
R-square: 1
Adjusted R-square: 1
RMSE: 4.342
可得到拟合函数为：
y=-0.0833*x^3.005 +11.88;

追问

谢谢你回答，能具体的再请教你一下用matlab工具箱怎么进行拟合，另外得到的
y=-0.0833*x^3.005 +11.88;代入程序运算也没有结果哦

追答

呵呵，如果你要求不高的话，其实y=-0.0833*x^3.005 +11.88中的x的次方可以直接减少为3次方，这样的话手工都可以求反函数的噢。