� f
1 ( x)
� exists only when f( x ) is one-to-one in the restricted domain
� Absolute function : � f ( x) if x � 0 f( x)
� � � � f ( x) if x � 0
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Exponential and Logarithmic Functions
x
� y� a : Exponential function of base a � 1
� Methods of solving an exponential equation 1 . Change b into y a such that 2 . Take logarithm for both sides x a � b: x y a � a � x � y
� y� log a x: Logarithmic function of base a � 0
� log log10 y � x � x : Common Logarithmic function
� y �ln x � log e x : Natural Logarithmic function , where e � 2.71828 ... is an exponential number
� Laws of logarithm , where a , b , c , p , q , x � 0 :
y 1 . x � a � y � log x 2 . log a
1� 0
3 . log a � a
1 4 . log p �log q � log pq a a a
5 . log p�log q� log a a a
n
6 . log p � nlog p
7 . log a
b logc a a � log b c a a p q
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