Mathematica Finding the range of the paramter space in Mathematica

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To determine the ranges of parameters a and b for the function f[a, b] such that 300 < f[a, b] < 400 in Mathematica, it is suggested to solve the equations f[a, b] = 300 and f[a, b] = 400 for one of the parameters. This approach helps identify the boundaries of the parameter space. Additionally, plotting the function with the condition 300 < f[a, b] < 400 can provide a visual representation of the valid parameter ranges. However, it is noted that finding an analytic solution for the inequalities may not be feasible.
Safinaz
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If I have a function depends on for example 2 parameters f[a,b], and I know the value of this function should range between 300 < f < 400, how I know the possible ranges of the parameters in Mathematica.

Bests,
S.S.
 
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You want to find the part of the parameter space of (a,b) where the function satisfies those inequalities?
In general, that does not have an analytic solution, but you can try to solve f(a,b)=300 and f(a,b)=400 for either a or b, then you can calculate and draw the boundaries. Alternatively, plot f - but only if 300 < f < 400. That gives you a graphical representation.
 
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