Question

Which function has an inverse that is also a function?
g(x) = 2x – 3
k(x) = –9x2
f(x) = |x + 2|
w(x) = –20

Answer 1

g(x) = 2x − 3.

Reason: g is one-to-one (strictly increasing), so it has a functional inverse. Solve y = 2x − 3 for x: x = (y + 3)/2, so g⁻¹(x) = (x + 3)/2.

The others are not one-to-one:
- k(x) = −9x²: k(2) = k(−2), so no inverse function.
- f(x) = |x + 2|: f(0) = f(−4), so no inverse function.
- w(x) = −20 (constant): many x map to the same value, so no inverse function.