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

1 Answer
Shwetank Mauria
Sep 24, 2017

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.

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