Practice question · Numerical answer
Let f have domain {-2, -1, 0, 1, 2} and rule f(n) = n squared. How many distinct elements are in its image?
Hints
- Compute every output, then discard repeats, the image is a set.
- Squaring loses the sign, so some inputs collide.
Show the answer
3
Why
The outputs are 4, 1, 0, 1, 4, so the image is {0, 1, 4}, three elements. The domain has five elements but the image only three, which is exactly the failure of injectivity made visible.
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