Question

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

Answer 1

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.

Answer 2

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.