2.7 Inverse Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
4.4 Exponential and Logarithmic Equations Functions
100
Are f(x)=x-4 and g(x)=2x+4 Inverses? Why?
They are not Inverses, f(g(x)) and g(f(x)) does not equal x
100
if f(x)=3x, what is f(x) if x=-3
f(x)=1/27
100
Write the equation log(217)=x as an exponent.
10x=217
100
expand log(100x)
2+log(x)
100
solve 5(x-6)=125
x=9
200
What is the inverse of f(x)=2x+7?
f-1(x)=(x-7)/2
200
if f(x)=1144e0.0325x, what is f(x) when x=36?, round to the nearest whole number.
f(x)=3686
200
Write 4y=614 in log form.
log4(614)=y
200
expand ln√x
½ln(x)
200
solve 8x+2=4x-4
x=-14
300
Give an example of a graph that passes the horizontal line test.
300
Find the accumulated value of an investment of $1200 if it is invested for 6 years at an interest rate of 6% and the money is compounded continuously.
$1720.00
300
SOLVE log36(6)
1/2
300
expand log5(√x/(25y3))
½log5(x)-2-3log5(y)
300
solve 7e2x=63
ln(9)/2 or 2ln(3)/2
400
Find the inverse of f(x)=½x-4
f-1(x)=2x+8
400
Find the accumulated value of an investment of $8500 if it is invested for 3 years at an interest of 4.25% and the money is compounded semiannually.
$9642.98
400
what is the domain of f(x)=ln(x-9)
domain is (9, ∞)
400
Write as a single logarithm:
3ln(x)+5ln(y)-6ln(z)
ln((x3y5)/z6))
400
solve ln(x)+ln(x-3)=1
5
500
f(x)=(2x-3)/(x+1) find the inverse
f-1(x)=(x+3)/(2-x)
500
The function f(x)=574(1.026)x models the population of India, f(x), in millions, x years after 1974. Find India's population, to the nearest millions in 2032.
2544 million
500
evaluate log619(1)
0
500
use the change of base formula to evaluate log7(2506), round to 2 decimal places.
4.02
500
Solve 4x+7=10
x=ln(10)/ln(4)-7