Intermediate Mathematics - Graphs of inverse functions
Graphs of inverse functions
The graphs of inverse functions are obtained by reflecting the graph of
the original function in the line y = x. Remember that for the inverse
function to exist as a function, the original function must be a one-to-one
function. Therefore you must check the original function and, if necessary,
restrict its domain. The range of the inverse function is equal to the
domain of the original function and the domain of the inverse function is
equal to the range of the original function. Thus:
ran_f_(x) = dom_f_(x)
dom_f_(x) = ran_f_(x)
* First sketch the graph of _f_(x) and the line y = x.
* for appropriate points (a, b) on the graph of f(x), plot the image
points (b, a) on the graph of f(x), plot the image points (b, a). Thus,
points on the X axis, (a, 0), reflect onto points on the Y axis, (0, a),
and vice versa. Points on the line y = x map onto themselves.
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