Chapter 11 Flashcards
Inverse of f(x)
F-1(x)
One-to-one function
In a one-to-one function, each x value corresponds to only one y value and each y value corresponds to only one x value
Inverse function
If (x,y) is in function f, then (y,x) is in the inverse of function f. The domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.
Horizontal line test
Used on graphs to determine if a function is one-to-one
Find the inverse of f(x)=2x-6
F-1(x)= (x+6)/2
Exponential function
F(x)=a^x
A is greater than 0 and not 1, for all real numbers x
Domain of an exponential function
All real numbers
Range of exponential functions
(0, infinity)
Property for solving exponential equations
A is positive and not 1:
If A^x=A^y, then x=y
Compound interest formula
A(t)=P(1+r/n)^nt
A: amount investment is worth after t years
P: principal investment
r: interest rate
n: number of times per year that the interest in compounded
Exponential growth/decay formula
P(t)=Pe^rt
P(t): growth or decay after t years
P: original amount
r: growth/decay rate
Logarithmic form
Y=log. x
a
Y= exponent
a: base
X:a^y
Convert log. 32=5 to exponential form
2
2^5=32
Exponential form
X=a^y
Meaning of log. x
A
The exponent to which base a must be raised to obtain x
Log. b=?
b
1
Log. 1=?
b
0
Logarithmic function
G(x)=log. x
a
Product rule of logarithms
Log. xy= log. x+log. y
b. b. b
Quotient rule of logarithms
Log. X/y= log. X-log. y
b. b. b
Power rule of logarithms
Log. X^r=rlog. X
b. b
B^(log. X)=?
B
X
Log. B^x=?
X
X
Common log
Log x is written as logx
10
Natural log
Log. X is written as lnx
e
If x=y, then…
B^x=B^y
If b^x=b^y, then…
x=y
If x=y, then…
Log. X=log. Y
b. b
If log. X=log. Y, then…
b. b
X=y
Change of base formula
Log. X= (log. X)/(log a)
a. b. b
