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

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Answer 1 · 2017-01-16T22:42:41

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

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#.