Answer:
(x - 1) / 3
Explanation:
To find the inverse of f(x) = 3x + 1, we need to rewrite the equation in the form y = f(x) and then solve for x in terms of y. The inverse function is then obtained by switching the roles of x and y.
Now we can solve for x in terms of y by subtracting 1 from both sides of the equation:
y - 1 = 3x + 1 - 1
y - 1 = 3x
x = (y - 1) / 3
Therefore, the inverse of f(x) = 3x + 1 is given by:
f^-1(y) = (x - 1) / 3
To check if the inverse is a function, we need to make sure that for every value of y, there is only one corresponding value of x. In this case, the inverse function f^-1(y) = (x - 1) / 3 satisfies this condition, so it is a function.