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A function f has domain [-1,2] and rang ...

A function `f` has domain `[-1,2]` and rang `[0,1]` . Find the domain and range of the function `g` defined by `g(x)=1-f(x+1)dot`

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The correct Answer is:
Domain: [-2, 1]; Range: [0, 1]
g(x) is defined if `f(x+1)` is defined .
Hence, the domain of g is all x such that `(x+1) in [0, 2],` i.e.,
`-2 le x le 1`.
Also, `f(x+1) in [0,1]`
` :. -f(x+1) in [-1,0]`
` :. 1-f(x+1) in [0,1]`
Therefore, range of g(x) is [0, 1].
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