How do you find the inverse of f(x)=3x+1 and graph both f and f^-1?

1 Answer
Jan 16, 2017

The inverse of f(x) = 3x + 1 is f(x)^-1 = 1/3x - 1/3.

Explanation:

In order to find the inverse of a function, all you have to do is switch where x and y are and resolve for y.

So after switching x and y,
y = 3x + 1
becomes
x = 3y + 1.

Now, we solve for y regularly.

3y = x - 1

y = 1/3(x - 1)

y = 1/3x - 1/3

f(x)^-1 = 1/3x - 1/3.

When the two equations are graphed, they will show symmetry along the line y = x.