# chapter 4 theories

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1. DEFINE:
One-to-one Function
f(a) = f(b) only when a = b.
2. DEFINE:
Inverse Function
If the ordered pairs of a function g are the ordered pairs of a function f w/ the order of the coordinates reversed, then g is the inverse function of f.
3. DEFINE:
Exponential Function
The exponential function w/ base b is defined by f(x)=bwhere > 0, b != 1, and x is a real number
4. DEFINE:
Logarithmic Function
• If x>0 and b is a positive constant except for 1 (b!=1), then y=logbx iff by=x.
• ***********
• 1. logbb = 1
• 2. logb1 = 0
• 3. logbb= x
• 4. blogb= x
5. LAWS OF LOG.s:
1. Product Property
• logbM*N = logbM + logbN
• ************
• let logbM = x and logbN = y,
• then bx = M and by = N.
• bx * by = M*N (multiplication prop.)
• bx+y = MN (product law of exponents)
• logbMN = x + y (substit. from the beginning)
• logbMN = logbM + logbN (substit.)
6. LAWS OF LOG.s:
2. Quotient Property
logb(M/N) = logbM - logbN
7. LAWS OF LOG.s:
3. Power Property
• logbMP = P * logbM
• ************
• let logbM = x
• then bx = M
• (bx)P= MP
• bx*P = MP
• logbMP = xP
• logbMP = P(logbM) (substit.)
8. LAWS OF LOG.s:
4. Change of Base Property
• If x, a, and b are positive real numbers w/ a != 1 and b != 1, then
• logbx = logax
•              logab
• ************
• logbx = y --> b= x
• logaby = logax
• ylogab = logax
• y = logax
•       logab
• logbx = logax
•              logab

## Card Set Information

 Author: jlane799 ID: 259863 Filename: chapter 4 theories Updated: 2014-02-03 00:49:29 Tags: functions math theories logarithms Folders: Ma105 Transcendental Functions Description: math function theories to know for Monday's test Show Answers:

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