In symbolic expression how to include an expression that is a function of the symbolic variable?

I have an expression given as e.g.:

g = @(x) f*x

where f is a function of x and is defined as

f(x) = b   if   x > a
f(x) = c   if   x <= a

and a,b,c are constant numbers.

1. How to define this function? How can a parameter depend on the symbolic variable in a symbolic expression?

2. How can I multiply two expressions like this? What I want to get is:

g = @(x) a*x;
h = @(x) b*x;
gh = g*h; % I want to get gh = a*b*x^2;

It gives an error saying

"Undefined function 'mtimes' for input arguments of type 'function_handle'."

I also tried gh = @(f) g*h, which also doesn't work.

Answer 1

[Mischa Kim]

László, try

 g =  @(x) x*(c*(x<=a) + b*(x>a));

and

 gh = @(x) g(x)*h(x);

[László Arany]

Thank you, these work nicely and the first one is very elegant!

However, what if I have a more complicated function? Say I have to solve the dispersion relation inside the symbolic expression?

H = @(f) k*f;

where k = k(f) and it results from the nonlinear expression f^2 = k*g*tanh(k*S) with g=9.81; S=21? Can I solve this more complicated nonlinear equation inside a symbolic expression somehow?

[Mischa Kim]

I believe this one is similar to the other question I just answered, unless you mean something different by solve...