Practice question · Multiple choice
The rule "send x to its square root" is not a function on the reals, but √x is. What was fixed?
Hints
- Try x = −4. Now try x = 9, and list every number whose square is 9.
- A function needs at least one output and at most one. Which failure does each x illustrate?
Show the answer
D. Two things: the domain was restricted and one branch was chosen
Why
−4 breaks totality and 9 breaks uniqueness, so both halves of the definition were violated by one rule. √ repairs both, which is why √9 is 3 and not ±3, and why the ± has to be written explicitly when solving x² = 9. The notation is carrying a decision.
Practise Functions as Mappings
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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.
- 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.
- Complete the definition of an injective function.