How do you solve this math problem?

Question

Is the following function invertible? If so, find its inverse
q(w) =2/1-x

Answer 1

if so...

q(w) = same as y

y = 2/1-x
x = 2/1-y
x(1-y) = 2
x - xy = 2
-xy = 2 - x
y = (2 - x)/-x

q-1(x) = (2 - x)/-x

Answer 2

I assume you mean

y = q(w) = 2 / (1 - x)

This function is invertible. It is similar to the function y = 1/x which is invertible.

Switch x and y and solve for y.

x = 2 / (1 - y)
x(1 - y) = 2
1 - y = 2/x
-y = 2/x - 1
y = -2/x + 1 = (-2 + x)/x
y = (x - 2)/x

The inverse is

q^(-1) (x) = (x - 2)/x