The function f from R to R is given by f:x↦x2+2x+2. Find the range of f, and state, with a reason, whether or not f is bijective.
The range of f is denoted by S, and the function g from S to R is given by g:x↦1/x. State the image of x under the composite function g∘f, and give the range of this composite function.
R′ denotes the set of real numbers excluding 0 and 1. Functions ϕ and ψ from R′ to R′ are given by ϕ:x↦11−x,ψ:x↦1−x.
Give in a similar form the definitions of ϕ−1 and (ϕ∘ψ)−1.