Inverse
Functions – Examples
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Recall the strategy to
find the inverse function of a one-to-one function, f(x) is: Switch
x and y Solve for
y in terms of x
(if possible) The resulting inverse
is f -1(x) = y |
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Example Find the inverse function
for y = ex . y
= f(x) = ex
note: for each value of x
there is only one value of f(x) x
= ey switch x
and y ln x = ln (ey) = y so
y = ln x = f -1(x) note:
restriction x ≥ 0 for log function |
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Other inverses: y
= tan-1(x) if and only if tan y
= x and
–π/2 < y
< π/2 y
= sin-1(x) if and only if sin y
= x and
–π/2 < y
< π/2 y
= sec-1(x) if and only if sec y
= x and
0 ≤ y
≤ π |
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Example of a function that has no inverse. It is NOT one-to-one. i.e.
for each value of x
there are two values of y (±) y2 =
x A parabola about
x-axis |
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Click here for another
example. Click here for an example
showing the derivative of an inverse function. |
| Return to Notes for Calculus 1 |
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