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Find range of the function f satisfying `(2007)^(x) + (2007)^(f(x)) = 2007`

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We have `(2007)^(x) + (2007)^(f(x)) = 2007`
`rArr x = log_(2007)(2007 - 2007^(f(x)))`
In order that x is defined in its domain we must have `2007 - 2007^(f(x)) gt 0`
`rArr 2007 gt 2007^(f(x))`
`rArr 2007^(f(x)) lt 2007`
`rArr f(x) lt log_(2007) 2007 = 1`
Hence `R_(f) = (-oo, 1)`
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