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Calculus I Quiz
#8 April
16, 2004

Name_________________ R. Hammack Score
______

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(1) Find the inverse of the function

Now interchange x and y.

(2) Explain why the function
is invertible.

Note that the derivative
is positive for all values of x.

Therefore the function g always increases,
and never decreases.

Thus it passes the Horizontal Line Test, so it is invertible.

(3) Consider the invertible
function ,
from the previous question.

Find the value of x for which .

Notice that ,
which means ,
which is the same as .

Thus x = 4.

(4) The graph of a one-to-one
function is drawn. Draw the graph of its inverse.

We just reflect this graph across the line y=x,
as illustrated.