A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?
Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
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