Multiplying f(x) with f(-x)

I need to write a code that will multiply function f(x) with f(-x)

Function is always inputed by user in form of an array.

coefficients = input('Enter the coefficients of the function with [ ] around them');

example: If user inputs [1 15 7 2] I would want to mutliply with .

Is there any way for this to be doen without writting a tone of code?

Thank you

Answer 1

[VBBV]

cof = [1 15 7 2]

cof = 1×4

1 15 7 2

syms x F(x)
F = (cof(1)*x.^3+cof(2)*x.^2+cof(3)*x+cof(4))

F = 

FF = subs(F,x,-x)

FF = 

Fx = F.*FF   % resulting product 

Fx = 

Fx = simplify(Fx)

Fx = 

[Omar Decevic]

Thank you!

Answer 2

[Sam Chak]

Hi @Omar Decevic

You can try this and take over from here:

x = -16:0.01:16;
f = @(x) x.^3 + 15*x.^2 + 7*x + 2;
plot(x, f(x).*f(-x), 'linewidth', 1.5)
grid on
xlabel('x')
ylabel('y')
title('f(x)*f(-x)')

Answer 3

[Bruno Luong]

For polynomial funtions with coefficients in P, f(x)*f(-x) is a polynomial as well with coefficients Q that can be computed like this

P=[1 15 7 2];

Pm=P.*(-1).^(length(P)-1:-1:0);
Q=conv(P,Pm)

Q = 1×7

-1 0 211 0 11 0 4

hold on; ezplot(@(x)polyval(P,x).*polyval(P,-x)); ezplot(@(x)polyval(Q,x));