Question

What does Inverse mean?

Answer 1

Hint: As per the given question we have to explain what the inverse word means in Mathematics. We can say that inverse in terms of mathematical language refers to the opposite of another operation. It is used in various mathematical terms and almost used in all new topics . We can understand it by taking some of the examples.

Complete answer:
We know that addition means to find the sum and subtraction means taking away or reducing. So we can say that subtraction is the opposite of addition or Subtraction is the inverse operation of Addition.
Similarly multiplication is repeated addition. It means that the same number gets added repeatedly while division is repeated subtraction. We can say that division is the inverse operation of multiplication.
Another is Multiplicative Inverse. It is a number which when multiplied by a number gives $ 1 $ as the product. For example $ a \times \dfrac{1}{a} = 1 $ . So here $ \dfrac{1}{a} $ is the multiplicative inverse of $ a $ .
We can say that inverse function is also known as anti-function which is defined as the function which can reverse into another function that means if the function accepts a certain value or performs a particular operation on the values and generates an output then the inverse function agrees with the result.
Basically an inverse function undoes the original function by switching the input and output. If there is function $ y = f(x) $ , then the inverse function would be $ x = {f^{ - 1}}(y) $ .

Note: We should note that reciprocal and inverse are two terms. A reciprocal can be an inverse but an inverse cannot be a reciprocal . A reciprocal is a multiplicative inverse. Also we can represent a reciprocal in different ways but it does not have any specific sign whereas an inverse is represented as $ {f^{ - 1}}(x) $ .