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tekilochka [14]
3 years ago
15

Which function, g or h, is the inverse of function f, and why?

Mathematics
2 answers:
raketka [301]3 years ago
6 0

An inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function f^{-1} to y gives the result x, and vice versa, i.e., f(x) = y if and only if f^{-1}(y) = x.

One of the main properties of function and its inverse function is:

  • If f and f^{-1} are inverses of each other then their graphs are reflections of each other across the line y = x.

From the diagram you can see that blue and red curves are reflections of each other across the line y = x, then the function h is the inverse, because for every point (x, y) on the graph of f, there is a corresponding point (y, x) on the graph of h.

Answer: correct choice is B.

earnstyle [38]3 years ago
5 0

The graph of a function and its inverse function are symmetric about the line y=x

On the graph above, I made a line y=x using green color.

The function h(x) is the inverse of f(x) because it is symmetric about the line y= x.

Hence option number B is correct.

Thus, The function h is the inverse because for every point (x, y) on the graph of f, there is a corresponding point (y, x) on the graph of h.

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