Logarithmic and Exponential Equations and Functions
Properties of Logarithms
Financial Models
100
EVALUATE A COMPOSITE FUNCTION
f(x)=2x and g(x)=x^2
(fºg)(1)=?
(fºg)(1)=f(g(1))=f(1)=2
100
DETERMINE WHETHER A FUNCTION IS ONE-TO-ONE
(-2,6),(1,3)(-1,0),(2,8),(0,5),(3,3)
it is not a one-to-one function because there are two different inputs that correspond to the same output.
100
a^s•a^t=?
a^(s+t)
100
logbB=?
1
100
what is the formula for simple interest
I=Prt
200
FIND THE DOMAIN OF THE COMPOSITE FUNCTION
f(x)=3x+1 and g(x)=x^2
what is the domain of the composite function (fºg)(x)?
all real numbers.
200
find the inverse of the following one-to-one function
(3,2),(-2,1),(0,3)
(2,3),(1,-2),(3,0)
200
a^(-1)=?
1/a
200
5^(log5 10)=?
10
200
what is the formula for continuous compounding ?
A=Pe^rt
300
FIND THE COMPONENT OF A COMPOSITE FUNCTION
H(x)=√(x^2+1)
what are the components of H(x)?
f(x)=√(x) and g(x)=x^2+1
300
finding the inverse functions
g(x)=x^3
g-1(x)=3rt(x)
300
what are the intercepts of y=a^x, where "a" is constant and x variable?
no x-intercept, y-intercept is 1
300
log of a product equals the sum of the logs
log5(24)=?
log5 4+log5 6
300
what is the formula for compound interest formula
A=P•(1+r/n)^nt
400
SHOW THAT TWO COMPOSITE FUNCTIONS ARE EQUAL
f(x)=3x-4 and g(x)=(1/3)(x+4)
for two functions to be equal, (fºg)(x) =(gºf)(x) = x
(fºg)(x) = f(g(x)) = f((x+4)3) = 3((x+4)/3)-4 = x
(gºf)(x) = g(f(x)) = g(3x-4) = (1/3)((3x-4)+4) = x
∴ they are equal.
400
verifying inverse function
f(x)=x^3, g(x)=3rt(x)
g-1(g(x))=x,
g(g-1(x))=x
so they are inverse functions.
400
what are the intercepts of f(x)=logaX, where a is constant and x variable?
x-intercept is 1, no y-intercept.
400
change of base formula
log3 5=?
log10 5/log10 3
400
someone invest $1000 at an rate of 10% compounded quarterly, what would he have after 5 years?
A=1000(1+0.1/4)^20
=1638.6 ($)
500
FIND THE DOMAIN OF THE COMPOSITE FUNCTION
f(x)=1/(x+2) and g(x)=1/(x-4)
domain of (fºg)(x) is?
domain of g(x) is x≠1,
domain of f(x) is x≠-2, solve g(x)=-2, x≠-1
∴ domain of (fºg)(x) is x≠-1, 1
500
graphing
f(x) and its inverse are symmetric according to ? (which line)
y=x
500
finding inverse of logarithmic function
f(x)=3log(x-1), f-1(x)=?
f-1(x)=10^(x/3)+1
500
solve
2^x=7
ln2^x=ln7
xln2=ln7
y=ln7/ln2
500
someone put $1000 at an annual rate of 10% compounded continuously, what would he have after 10 years?