Inverse functions
The Maths Habit
5 → × 4 → − 3 → ? Find the output.
17−2 → + 6 → × 3 → ? Find the output.
12? → × 2 → + 9 → 25 Find the input.
8
A present: box it, wrap it,
then stick on a bow.
How do you open it?
Bow, wrapping, box:
the last step first
- Inverse function
- The function that undoes another: it takes the output back to the input.
Find f−1(x)
f(x) = x + 4
x − 4
f(x) = x − 9. Find f−1(x).
x + 9f(x) = 6x. Find f−1(x).
x6f(x) = x3. Find f−1(x).
3xf(x) = x + 12. Find f−1(20).
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Undo both, in order
× 2, then + 7
− 7, then ÷ 2
f(x) = 4x + 3. Find f−1(x).
x→× 4→+ 3→f(x)f−1(x)←÷ 4←− 3←x
f−1(x) =x − 34
f(x) = 2x − 7. Find f−1(x).
x→× 2→− 7→f(x)f−1(x)←÷ 2←+ 7←x
f−1(x) =x + 72
f(x) = 4x + 3. Find f−1(x).
x→× 4→+ 3→f(x)f−1(x)←÷ 4←− 3←x
f−1(x) =x − 34
f(x) = 6x + 1. Find f−1(x).
x→× 6→+ 1→f(x)f−1(x)←÷ 6←− 1←x
f−1(x) =x − 16
f(x) = 3x − 4. Solve f−1(x) = 5.
x = 11Which function is its own inverse: f(x) = x + 1, f(x) = 10 − x or f(x) = 2x?
10 − x
f(x) = 8x. Find f−1(x).
f−1(x) = x8f(x) = 5x − 3. Find f−1(x).
f−1(x) = x + 35f(x) = 4x + 7. Find f−1(27).
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Exit tickets to print
