Please show clear workings and steps and answer the questions Correctly.

The ceiling of a real number r, denoted , is the unique integer that satisfies The absolute value of a real number a, denoted lrl, is defined as z when r 20 -z when0 Z is the set of integers. R is the set of real numbers. 1. Determine whether or not the following functions from R to R are bijections. If they are bijections, then find the inverse. If they are not bijections, then explain why not. (a) Jr) [2r] (b) f(x)=-7z (c) f(z) 73-5 (d) f(x) - 2r -1 (e)/(z) =2-5