Let f(x)=4-x, x in R. Find its inverse and sketch both graphs with y=x. Find the point where f(x)=x.

Question

Let f(x)=4-x, x in R. Find its inverse and sketch both graphs with y=x. Find the point where f(x)=x. Explain whether this is the only point shared by the function and inverse graphs.

Accepted Answer

$\mathrm f^{-1}(x)=4-x$; fixed point $(2,2)$; the entire line $y=4-x$ is shared.

A decreasing self-inverse graph

A decreasing self-inverse graph

Solution:

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