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

Answer

Domain: [-2, 1]; Range: [0, 1]

Explanation

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].