MATLAB: How to convert different variables into one unified variable in a function

Question

Hello I'm a newbie with matlab. Thanks for reading this post.

So I have function f (x,y,z,r) = (x^2 + y^2 +2z)*r

Then I also have z = (x^2+y^2) +2

and r = sqrt(x^2+y^2)

So how do I convert them all into r ? So that my new function f( r ) only have one variable r

f( r ) = (3*r^2 +4)*r

Thank you so much for taking time skimming through this post.

Answer 1

syms x y z r
z =  (x^2+y^2) +2
fxyz = (x^2 + y^2 +2*z)*r     %uses definition of z in terms of x y
eqn = r == sqrt(x^2+y^2)
rx = solve(eqn, x)            %define x in terms of r
fr = simplify(subs(fxyz, x, rx))   %substitute definition of x. Simplify