Scan over regions of parameters

Question

I have a function f which takes three arguments x, y and z:

 f[x_,y_,z_] := 2 x + 0.5 y + z

The arguments x, y and z must have a pre-defined domains, for example:

 -1 < x < 1
  3 <= y < 7
 -3 < z <= 3

I would like to run my function across x,y and z sets corresponding to some pre-defined domains as stated above and extract only those x, y and z sets which produce some arbitrary value, for example:

7, 12, 20 etc.

The expected output I seek is something like:

{{x,y,z}, result}

where {x,y,z} is a set of x,y,z arguments which were passed to my function and result is the associated result which is some pre-defined arbitrary value.

Edit

If I have a function in four parameters instead as f[x_,y_,z_,d_] := 2 x + 0.5 y + z+ d

and I want to run f only over x,y,z regions while fix d at say d=5 . I tried:

f[x_, y_, z_, d_] := 2 x + z + 0.5 y + d

x := Range[1, 5, 1]
y := Range[5, 9, 1]
z := Range[10, 14, 1]
d := 5

data = Outer[f, x, y, z, d]

But it gave output sample:

{{{f[1, 5, 10], f[1, 5, 11], f[1, 5, 12], f[1, 5, 13], f[1, 5, 14]}}}

So it seems doesn’t work. Any help ..

Note that I don't want to set d from the pre definition of the function, because my real calculation are so long and will be difficult to define the fixed parameter each time .

Answer 1

Example:

(*arbitrary data*)
x = Range[1, 5, 1]
y = Range[5, 9, 1]
z = Range[10, 14, 1]

{1, 2, 3, 4, 5}
{5, 6, 7, 8, 9}
{10, 11, 12, 13, 14}

(*process*)
data = Outer[f, x, y, z];

Output (sample):

Domain: {1,5,10}, {1,5,11}, {1,5,12}, {1,5,13}, {1,5,14}

EDIT 1

This way may be not the best way how to achieve what you are after. There are some brilliant people out here who can do it with much better aesthetics and efficiency.

domains = Flatten[Outer[List, x, y, z], 2];
results = Flatten[Outer[f, x, y, z], 2];

Select[Transpose[{results, domains}], #[[1]] >= 20 &]

EDIT 2

If you decide to include any additional argument:

Declare domain of interest:

 d = Range[15, 19, 1]

The rest is the same:

domains = Flatten[Outer[List, x, y, z, d], 2];
results = Flatten[Outer[f, x, y, z, d], 2];

Select[Transpose[{results, domains}], #[[1]] >= 20 &]

NOTE:

Make sure to include d in your function declaration!

Reference

Outer + Animation