Explanation:

First, let's define what it means for a function to be a bijection. A function f(x) is a bijection if it is both injective and surjective.



Injective:
A function f(x) is injective if it maps distinct elements of the domain to distinct elements of the range. In other words, for any two different x values, f(x) will produce two different y values. Mathematically, if f(x1) = f(x2), then x1 = x2.



Surjective:
A function f(x) is surjective if every element in the range has a corresponding element in the domain. In other words, for every y value in the range, there exists an x value in the domain such that f(x) = y.



Now, let's consider the inverse of a bijective function, f-1(x). The inverse function swaps the domain and range of the original function. In other words, if f(x) maps x to y, then f-1(x) maps y to x.



Mirror Image:
When we say that f-1(x) is a mirror image of f(x) around y = x, we mean that the graph of f-1(x) is the reflection of the graph of f(x) across the line y = x. This means that the points on the graph of f(x) and the points on the graph of f-1(x) are symmetric with respect to the line y = x.



Explanation of the Answer:
Since f(x) is a bijection, it is both injective and surjective. This means that for any two different x values, f(x) will produce two different y values, and every y value in the range has a corresponding x value in the domain. Therefore, the points on the graph of f(x) are symmetric with respect to the line y = x.



When we take the inverse of f(x) to get f-1(x), we are swapping the domain and range. This means that the points on the graph of f-1(x) will be the reflection of the points on the graph of f(x) across the line y = x. Therefore, f-1(x) is indeed a mirror image of f(x) around y = x.



Therefore, the correct answer is option 'A' - True.