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Is the invertible to be one to one function?
Yes, a function needs to be one-to-one in order to have an inverse.
What is the answer of opposite or inverse?
Two operators are opposites or inverses if their combined mapping is the identity mapping. Less technically, one mapping must reverse the effect of the other. There are problems, though, when dealing with even fairly common functions. Squaring is a function from the real numbers to the non-negative real numbers, but there is not a single inverse operation. [+sqrt and -sqrt are the two inverse functions over the range.]
What is the range of the inverse of relation (1 7) (2 -4) (5 6) (2 8)?
The original relationship is one-to-many. It is therefore not an invertible relationship.
Is the inverse of the function y x2 still a function?
Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
Is a to power of 4 multiplied by b to power of 5 invertible?
Indeterminate. How? a4b5 is the expression instead of equality. Since we are not given the equality of two variables, there is no way to determine whether it's invertible or not. Otherwise, if you are referring "a" and "b" as invertible matrices, then yes it's invertible. This all depends on the details.
