Question

determine if the given function is one-to-one. if it is, find the inverse.
f(x) = 8x - 4

A) f-1(x) = x+4 / 8
B) f-1(x) = x-4 / 8
C) Not one-to-one
D) f-1(x) = x/8 + 4

Answer 1

All functions that are strictly increasing or decreasing in its domain are one-to-one.
Since the given function has a constant positive slope, it is strictly increasing over ℝ, so it is one-to-one.

The inverse can be found as follows:
1. interchange x and y to get
from f(x) = y = 8x - 4
to
x=8y-4
2. Solve for y in terms of x:
8y=x+4
y=(x+4)/8

Now there is sufficient information to find the correct answer.