Question

Find the inverse of each of the following bijections. u: ℚ → ℚ , u(x) = 3x − 2.

a) v(x) = (x + 2) / 3
b) v(x) = (x - 2) / 3
c) v(x) = (x - 2) / 3
d) v(x) = (x + 2) / 3

Answer 1

The inverse of the function u(x) = 3x - 2 is v(x) = (x + 2)/3.

Step-by-step explanation:

To find the inverse of the function u(x) = 3x - 2, we need to solve for x in terms of u. Let's solve for x:

u(x) = 3x - 2

Add 2 to both sides to isolate the term with x:

u(x) + 2 = 3x

Divide both sides by 3:

x = (u(x) + 2)/3

So, the inverse of u(x) is v(x) = (x + 2)/3.

Therefore, for part (b) v(x) = (x - 2)/3 is not the inverse of u(x).