What must be true of a function before its inverse is also a function?
AIt must be a many to one relation
BIt must pass through the origin
CIt must be a one to one relation
DIt must be a straight line graph
Answer & Solution
Correct answer: C. It must be a one to one relation
1. Finding an inverse means swapping the input and output values around.
2. If two different inputs shared one output, the swap would give one input with two outputs.
3. That result would fail the definition of a function.
4. So the original function has to pair each output with exactly one input, which is a one to one relation.
5. A many to one relation is exactly the case that fails, so that option is wrong.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 2: Functions_
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