Inverse Functions
If f(2) = 5 find f-1(5)?
2
Solve for x: log2(x+3) - log2(x-1)=3
x=11/7
True or False: The sine value is the x-coordinate on the unit circle
False, the sine value is the y-coordinate while the cosine value is the x-coordinate on the unit circle
True or False: tan(θ) = sin(θ)/cos(θ)
True
Convert 4π/3 to degrees
240°
If f(x) = 2x+5 find its inverse g(x)
g(x) = (x-5)/2
Solve for x: log3(x-1) = 4
x=82
What are the coordinates at π/3?
(½, √3/2)
Given that cos(θ) =3/5 with θ in quadrant IV what is sin(θ), tan(θ), and csc(θ)?
sin(θ) = -4/5
tan(θ)=-4/3
csc(θ) = -5/4
Convert 330° to radians
11π /6
If f(x) = (x-2)/(3x+5) what is the inverse's range?
All real numbers except -5/3
f(x) = 3-3x-9, what is f(-3) and f(-11/3)
f(-3) = 1
f(-11/3) =9
What angle does (-√3/2, ½) denote in radians and degrees?
5π/6 =150°
Suppose we have side lengths 5 and 12 and the angle opposite of side length 5 is theta what is cot(θ), sin(θ), sec(θ)
cot(θ) = 12/5
sin(θ) = 5/13
sec(θ) = 13/12
Give me the reference angle for 138°.
42°
True or False: The range of a function is the same as the domain of its inverse function
True
e-15=1/e15
If θ=-5π/6 then what is csc(θ) equal to?
-2
y=7tan(3x)+8
Period and Asymptotes
Period = π /3
Asymptotes = π /6 +kπ /3
Expand log((2x3y2)4/(√(ab3)))
4log(2)+12log(x)+8log(y)-1/2 log(a)-3/2 log(b)
If f(x) = √ (3x+2) find the inverse g(x)
g(x) = (x2-2)/(3)
John deposits $8000 into an investment account that earns 6% annual interest compounded monthly. A) How much money will be in the account after 5 years? B) Suppose the bank instead compounds quarterly at the same 6% rate, how much money would John have after 5 years? C) Using the monthly compounding account, how long will it take for the investment to reach $12000?
A) $10790.80
B) $10774.84
C) 6.77 years
cot(π/6)sin(2π/3)
3/2
y=-4cos(2x+π ) + 1
Find the amplitude and the period
Amplitude =4
Period = π
Simplify 6log5(25) + (4log5(125))/(3log5(625))
13