Someone help me understand

f¯¹(x) = 23/ (6x + 3)

Step-by-step explanation:

f(x) = (23 – 3x)/6x

The inverse, f¯¹, for the above function can be obtained as follow:

f(x) = (23 – 3x)/6x

Let y be equal to f(x)

Therefore, f(x) = (23 – 3x)/6x will be written as:

y = (23 – 3x)/6x

Next, interchange x and y.

This is illustrated below:

y = (23 – 3x)/6x

x = (23 – 3y)/6y

Next, make y the subject of the above expression. This is illustrated below:

x = (23 – 3y)/6y

Cross multiply

6xy = 23 – 3y

Collect like terms

6xy + 3y = 23

Factorise

y(6x + 3) = 23

Divide both side by (6x + 3)

y = 23/ (6x + 3)

Finally, replace y with f¯¹(x)

y = 23/ (6x + 3)

f¯¹(x) = 23/ (6x + 3)

Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is

f¯¹(x) = 23/ (6x + 3)