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Combining Functions

Review question

Can we work with the domain, codomain and range of a bijection?

Ref: R5966

  1. The function f from R to R is given by f:xx2+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:x1/x. State the image of x under the composite function gf, and give the range of this composite function.

  2. R denotes the set of real numbers excluding 0 and 1. Functions ϕ and ψ from R to R are given by ϕ:x11x,ψ:x1x.

    Give in a similar form the definitions of ϕ1 and (ϕψ)1.