Finding Inverses Calculator

For example 2x + 3, (x - 5)/3, x^3 + 1, exp(x), ln(x), x*exp(x).
The engine returns the x with f(x) = y, i.e. f-inverse(y).
Interval used for the one-to-one check and for numeric inversion.
Sample points of f and its inverse (the inverse mirrors f in y = x).
f-inverse(y)
4
Inverse Function Calculator
Inverse function
(x - 3) / 2
Method used
symbolic
Check: f applied to the answer
11
One-to-one on the interval
yes - strictly increasing on [-50, 50]
Domain and branch notes
No domain restrictions were needed.
Verification residual
0
Worked out from OpenStax College Algebra, section 3.7 "Inverse Functions" and 2 other sources.

How this is worked out

5 steps
  1. Start from y = 2 * x + 3.
  2. Swap the roles of x and y, then undo each operation in reverse order.
  3. f-inverse(x) = (x - 3) / 2.
  4. Substituting x = 11 gives f-inverse(11) = 4.
  5. Check: f(4) = 11 (target 11).
Points on f and on f-inversetable
xf(x)inverse point xinverse point y
-33.333333-63.666667-63.666667-33.333333
-16.666667-30.333333-30.333333-16.666667
0330
16.66666736.33333336.33333316.666667
33.33333369.66666769.66666733.333333

Results are general information, not financial, tax, legal, medical or engineering advice.