equation solving - SolveAlways rejects inequality

I have two functions of x, f and g. f[x] = g[x] + 2, but the exact form of g[x] is unknown. It is known that g[x] is well-formed, positive, continuous, differentiable, etc., but an exact representation is unknown.

What I would like to find are the conditions under which f[x] is positive. This is clearly whenever g[x] > -2, however, when I use SolveAlways:

f[x_] = g[x] + 2
SolveAlways[f[x] >= 0, x]

I get:

SolveAlways::eqf: 2 + g[x] < 0 is not a well-formed equation. >>

Answer

SolveAlways is not used when inequalities are involved - see the documentation.

Reduce[f[x] == g[x] + 2 && f[x] > 0, Reals]

will give you what you want.

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