Question

For the function f(x) = (4 – 2x)2, find f–1 and the domain and range of f and f–1. Determine whether f–1 is a function.

Answer 1

f(x) = (4 - 2x)2 = 8 - 4x => A linear Function
f(x - 1) = [4 - 2(x - 1)]2 = (4 - 2x + 2)2 = (4 - 2x) + 4 = f(x) + 4 = 12 - 4x => A Linear Function
Domain [f(x)] = R
Domain [f(x - 1)] = R
where, R is for Real Numbers.