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For a one-to-one function f, f(3) = 11. What does the inverse function give for an input of 11?
AIt gives back 11
BIt gives back 14
CIt gives back 3
DIt gives a reciprocal
Answer & Solution
Correct answer: C. It gives back 3
1. An inverse function reverses the roles of input and output.
2. The original pairing sends the input 3 to the output 11.
3. So the inverse must send the input 11 back to the output 3.
4. Writing that in notation, f inverse of 11 equals 3.
5. Giving back 11 repeats the input rather than reversing the pairing.
6. Giving back 14 adds the two numbers, which no inverse rule does.
7. Giving a reciprocal treats the raised negative 1 as a power, but it is notation rather than an exponent.
_Source: OpenStax College Algebra (CC BY 4.0), section 3.7 Inverse Functions_