Question

Is the statement true: the graph of `f^-1` is obtained by reflecting the graph of the function f about the line y=x?

Answer 1

Yes, it is true but with some limitations.

Explanation:

We can obtain `f^(-1)(x)`, by replacing `y` with `x` and `x` with `y` and therefore reflecting the graph of the function `y=f(x)` about the line `y=x` gives the graph of `f^(-1)(x)`, but there could be some limitations.

For example, if `ffx)=4-x^2`, itsgraph and line `y=x` appears as follows:

graph{(y+x^2-4)(y-x)=0 [-10, 10, -5, 5]}

and graph of its inverse function `f^(-1)(x)=sqrt(4-x)` appears as

graph{(y-sqrt(4-x))(y-x)=0 [-10, 10, -5, 5]}

Observe that a part of te graph does not appear as for `x>4`, `sqrt(4-x)` is not defined.