equation solving - Solve `f(x)=0` with a parameter

I want to solve f(x)=0 with following code (with a parameter):

 $Assumptions = \[Lambda] > 0; 
    f[x_] := x - \[Lambda]*Cosh[x/4]; 
    FindRoot[f[x] == 0, {x, 0}]
    N[FindInstance[f[x] == 0, x, Reals, 2]]
    N[Reduce[f[x] == 0, x, Reals]]
    NSolve[f[x] == 0, x, Reals]
    N[Solve[f[x] == 0, x, Reals]]

But I do not have any solution. I can solve f(x)=0 for following code (without parameter):

f[x_] := x - Cosh[x/4]; 
FindRoot[f[x] == 0, {x, 0}]
N[FindInstance[f[x] == 0, x, Reals, 2]]
N[Reduce[f[x] == 0, x, Reals]]
NSolve[f[x] == 0, x, Reals]
N[Solve[f[x] == 0, x, Reals]]

Any suggestions?

Comments

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