Relations & functions
Types of relations, one-one and onto functions, composition and inverses.
Learn with Kutty
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An inverse function undoes what the function did.
Look: f sends 1 → 1, 2 → 4, 3 → 7. The inverse sends them back.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Inverse of f(x) = x + 5?
2Inverse of f(x) = 5x + 1?
3If f(x) = x + 1 and g(x) = 2x, find g(f(3)).
! Careful!
✗Undoing in the same order.
✓Undo in reverse: last step first.
✗f⁻¹ means 1/f.
✓It means the undo function.
See the whole lesson on one page
An inverse function undoes what the function did.
f(x) = 3x − 2 means "times 3, then take 2". To undo: add 2, then divide by 3. Undo in reverse order.
Think of it like thisLocking a box and unlocking it. Or putting on socks and taking them off. The second step undoes the first.
- f⁻¹
- The inverse: the undo function.
Solved together
Find the inverse of f(x) = 3x − 2.
f does: × 3, then − 2.
Undo backwards: + 2, then ÷ 3.
f⁻¹(x) = (x + 2) ÷ 3Check: f(4) = 10, and f⁻¹(10) = 12 ÷ 3 = 4. ✓
Answerf⁻¹(x) = (x + 2) ÷ 3.
For older learners and grown-ups: a little more
Only one-one and onto functions (bijections) have inverses. x² on all real numbers is not one-one (2 and −2 both give 4), so it has no inverse unless the domain is restricted to x ≥ 0.
Now practise it
Kanakku makes new questions on relations & functions every time. It shows the working and gives a hint when you are stuck.