Practice One-to-One Mapping in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A one-to-one (injective) function maps every distinct input to a distinct output — no two different inputs produce the same output.
No two inputs share the same output—like social security numbers.
Example 1
easyDetermine whether f(x) = 2x + 3 is one-to-one by (a) the definition and (b) the horizontal line test.
Example 2
mediumShow that g(x) = x^3 is one-to-one on \mathbb{R}, then find its inverse function.
Example 3
easyWhich functions are one-to-one? (A) f(x)=x^2 on \mathbb{R}. (B) f(x)=e^x. (C) f(x)=|x|.
Example 4
hardFind the inverse of h(x) = \dfrac{2x+1}{x-3} and state its domain.