If the subset y is the empty set, then the statement is false. That is the counterexample.
We know that for an invertible function, we always have that:
[tex]f(x) = y\\f^{-1}(y) = x[/tex]
Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:
f^{-1} is defined on b→a
Now we want to work on a subset y ⊆ b.
And here comes the problem.
The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.
If you want to learn more about inverse functions:
https://brainly.com/question/14899241
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