Find the inverse of the following function. g(x)= 1/x - 4
Please show all the steps used to find the answer.
To find the inverse of a function g(x), we can follow these steps:
Step 1: Replace g(x) with y.
y = 1/x - 4
Step 2: Swap the x and y variables.
x = 1/y - 4
Step 3: Solve the equation for y.
1/y = x + 4
y = 1/(x + 4)
Therefore, the inverse of the function g(x) = 1/x - 4 is h(x) = 1/(x + 4).