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If f(x)=(1)/(2)x-4 and f(g(x))=g(f(x)), ...

If `f(x)=(1)/(2)x-4` and `f(g(x))=g(f(x))`, which of the following can be g(x) ?
I. `2x-(1)/(4)`
II. `2x+8`
III. `(1)/(2)x-4`

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