Inverse functionsOne and two steps
Name: Date:
Find the inverse of each function.
1f(x) = x − 5
2f(x) = x − 39
3f(x) = 8x + 7
4f(x) = 4x
5f(x) = 7x − 6
6f(x) = x − 8
7f(x) = x + 57
8f(x) = 9x
Inverse functions worksheets
An inverse undoes a rule, and the way to find one is mechanical: write y, swap x and y, solve for y, call it f⁻¹(x). These free printable worksheets drill that sequence until the swap stops being the step people forget.
If they get stuck
Inverse functions
The answer key prints on a separate page.
What's on this sheet
The swap is the whole method and it is the line students skip. Skipping it means solving the original equation for x and writing that down — which looks like working, produces an expression, and is the wrong function. Every answer key here shows the swap on its own line for that reason.
Why this sheet works
Reading the operations off backwards is faster and is deliberately not what these sheets teach. “It multiplies then subtracts, so the inverse adds then divides” gets the right answer for f(x) = 3x − 5 and stops working the moment x appears more than once. The algebra does not.
How this one works
Find the inverse of f(x) = x − 5
x = y − 5
f⁻¹(x) = x + 5
- Write the rule as y = x − 5, then swap x and y. The swap is what makes it an inverse; everything after it is ordinary solving.
- Solve for y, then rename it: an inverse is written f⁻¹(x), so f⁻¹(x) = x + 5.