substituting functions in a function

I need to substitue funstions g(y) = (Wg/y)^2, h(x) = sqrt(1+g(sqrt(2)*x))+1/(sqrt(1+g(sqrt(2)*x))-1), V(z) = z-1/(z+1) and f(w) = sqrt(sqrt(w)+1/(sqrt(w)-1)) in final equation theta = ln(V[f(g(sqrt2)+1)]/V[f(g(Lg))]) + ln(h(2.3*t)/h(s)). I am using nested equation but not able to solve it. Please help.

Answer 1

[Walter Roberson]

You will need to check that I transcribed everything correctly.

syms Lg Wg s t w x y z
g(y) = (Wg/y)^2

g(y) = 

Root2 = sqrt(sym(2));
h(x) = sqrt(1+g(Root2*x))+1/(sqrt(1+g(Root2*x))-1)

h(x) = 

V(z) = z-1/(z+1)

V(z) = 

f(w) = sqrt(sqrt(w)+1/(sqrt(w)-1))

f(w) = 

Theta =  log(V(f(g(Root2)+1))/V(f(g(Lg)))) + log(h(sym(2.3)*t)/h(s))

Theta = 

simplify(Theta, 'steps', 50)

ans = 

[Marsha Parmar]

Thank you for the answer. But may be I was not able to explain my self clearly. There is a big theta equation which goes as,

θ_total=1/(πWg k) ln(V[f(g[√2 s])+1]/V[f(g[Lg ])] )+1/2πsk ln((h(2.3t))/(h(s))).

Here you can see that 'V' is function of 'f' which in turn is a function of 'g' etc. Now these functions are given as,

g(y)=(Wg/y)^2

f(w)= √((√w+1)/(√w-1) )

V(z)=(z-1)/(z+1)

h(x)= (√(1+g(√2 x))+1)/(√(1+g(√2 x))-1).

So now suppose I wish to substiute g in h(x), then it will be,

h(x)= (√(1+(Wg/(√2 x))^2 )+1)/(√(1+(Wg/(√2 x))^2 )-1)

which I have done manually. Now if I need to calculate,

V[f(g[√2 s]), where 'g' is function of √2 s, 'f' is a function of f(g[√2 s]), and then 'V' is afunction of V[f(g[√2 s]).

If there is a way to write down a cose to substitute these function into a bigger function it will be very helpful.

[Torsten]

But that's exactly what @Walter Roberson 's code does.

It defines functions g(y), f(w), V(z) and h(x) and computes a new function Theta by certain compositions of the functions previously defined.

[Marsha Parmar]

Yes, I got to see now. Thank you so much.