Difference between reciprocal and multiplicative inverse with example
Answers
Answer:
So, the additive inverse for a positive three is negative three and so on. On the other hand, the multiplicative inverse of a number is actually its reciprocal. For example, the multiplicative inverse (reciprocal) of 2 is ½. ... If you multiply 2 by ½, the answer is 1
Step-by-step explanation:
A reciprocal is a type of inverse, but an inverse is not necessarily a reciprocal.
The reciprocal of a number is its multiplicative inverse. If x is any non-zero number, then x⋅1x=1 .
It is also the case that we represent 1x as x−1 , and this points to a problem students often have with our math notation.
The inverse of a function f is another function g such that f(g(x))=g(f(x))=x . If f(x)=2x+3 , and if g(x)=x−32 , then f(g(x))=g(f(x))=x for any value of x you choose.
A huge problem arises at this point from our notation. People often think that math is crystal clear in its notation, but that's not always true. I learned from teaching it how our symbolism can get in the way of the ideas we are trying to express. This is a great example.
If g(x) is the inverse of f(x) we typically represent it as g(x)=f−1(x) . So in the example above, we would write f−1(x)=x−32 .
However, note that it is NOT the case here that f(x)⋅f−1(x)=1 !
Unfortunately that is where lots of confusion arises, mistakes are made, and students end up thinking math makes no sense.
There are other examples as well, but it is the case that our mathematical notation evolved historically, and being a human product, it is not always consistent.