11/28/11 f (x) = 3x − 5
f −1 (x) =
x +5
3
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
The function f gives an expression of y in terms
of x.

To find the inverse of f we need an expression
of x in terms of y:
◦  y=f(x)
◦  Solve for x!
◦  Since we usually consider x the independent, and y
dependent, we exchange y and x.
1 11/28/11   Find
inverse of
  If
a, x>0, and a ≠ 1, the logarithm of x
with base a is denoted by logax and is
defined as follows:
y = loga x
  loga x
if and only if
x=ay
= exponent needed on base a to
get x
2 11/28/11   Since
exponential and logarithmic
functions are inverse we have:
3 11/28/11 log a x =
log b x
log b a
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4 11/28/11 5 11/28/11 6 11/28/11 7 11/28/11 8 11/28/11 2[log 4 x − log 4 (x − 2)] =
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9 11/28/11 10 11/28/11 log 9 [(xy) 2 (x + 3) 4 ] =
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11 11/28/11 12 11/28/11 13 11/28/11 14 11/28/11 15