What is the inverse of f(x)=8x+14/2x+6?

(x-6)/15

Your notation is a little ambiguous though, do you mean (14/2)x or 14/(2x)?

Step-by-step explanation:

A function has one output for every input in the domain. The inverse function of a function takes every pair of input-output and flips the roles. So, (assuming function is one-to-one) if f(3) = 2, f^-1(2) = 3.

Ok, so we can apply that here. If, when x is inputted to the function, f(x) is returned, then in the inverse function, when f(x) is inputted, x should be returned.

That means that we can switch f(x) with x in the equation and f(x) with f^-1(x) and solve for f^-1(x).

x = 8f^-1(x) + 7f^-1(x) + 6

x-6 = 15f^-1(x)

(x-6)/15 = f^-1(x)