The inverse of this function would be f(x) = [tex] \frac{3}{-2x} + 2 [/tex]
To find this, we need to start by switching the f(x) and the x. When you've done so, you can then solve for the new f(x). That will be the inverse function. The work is done below here for you.
f(x) = [tex] \frac{3}{4 - 2x} [/tex] ----> switch f(x) and x
x = [tex] \frac{3}{4 - 2f(x)} [/tex] ----> multiply both sides by 4 - 2f(x)
x(4 - 2f(x)) = 3 ----> divide both sides by x
4 - 2f(x) = [tex] \frac{3}{x} [/tex] ----> subtract 4
-2f(x) = [tex] \frac{3}{x} [/tex] - 4 ----> divide both sides by -2
f(x) = [tex] \frac{3}{-2x} + 2 [/tex]
And that is the inverse function.
