Question

f^-1 (x)=(x-6)/3

find f(5)
find f^-1 (21)

explain

Answer 1

We are given f⁻¹(x) = (x − 6)/3.

Find f(x): set y = f⁻¹(x) = (x − 6)/3, swap x and y to get x = (y − 6)/3, then solve for y:
3x = y − 6 → y = 3x + 6.
So f(x) = 3x + 6.

Now compute:
- f(5) = 3(5) + 6 = 15 + 6 = 21.
- f⁻¹(21) = (21 − 6)/3 = 15/3 = 5.

Explanation: f and f⁻¹ undo each other, so if f(5) = 21 then f⁻¹(21) = 5. This matches the algebra above.