Practice question · Fill in the blanks
Complete the definition of an injective function.
A function is injective when different inputs always give ______.
Word bank: the same output · different outputs · every output in the codomain · at least one output
Hints
- Injective is also called 'one-to-one'.
- Equivalently: if two outputs are equal, the inputs must have been equal.
Show the answer
A function is injective when different inputs always give different outputs.
Why
Injective means distinct inputs give distinct outputs, equivalently, f(a) = f(b) forces a = b. Hitting every element of the codomain is a different property: surjectivity.
Practise Functions as Mappings
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Functions as Mappings
- Let f have domain {-2, -1, 0, 1, 2} and rule f(n) = n squared. How many distinct elements are in its image?
- Let f(n) = 2n with domain and codomain the integers. Select every integer that IS in the image of f.
- The rule "send x to its square root" is not a function on the reals, but √x is. What was fixed?
- A function must assign exactly one output to each input. Why does the "exactly one" requirement do more work…
- Order the steps of a proof that f(n) = 3n - 2 is injective.
- Every function from the integers to the integers is surjective.
- A function assigns exactly one output to each input. Sort each correspondence.