Math 1111 Review
(1/9^-2)^-1
Ans: 81
Solve this log equation: Log(b6)216 = 4x + 7.
x = -1
Convert Log. in to expo., y = log x
10^y = x
Solve x^2 + 3x = 4
= {-4, 1} (pg. 92-99)
3^-2 =
=1/9 (pp. 21-24 and page 73-77)
f(x) = ln(x+4); Find the following: domain, range, asymptotes, and inverse.
Domain: { x | x > -4}, Range: {all real} VA (vertical Asymptote at x = -4. Inverse: f^-1 = e^x - 4
ax^2 + bx + c = 0
Is a quadratic equation.
Convert expo. into log: 7^5 = 16,807
log (base 7)(16,807) = 5
Write the expression as a single log: 2log(base3)u - log(base3)v =
log(base3) (u^2/v)
Quadratic Formula:
x = (-b + or -)(sqrt. of b^2 -4ac)/(2a)
5^(5x + 1) = 125
x = 2/5
e^(3x) = 10 (solve for x):
x = ln(10)/3
Convert Log. in to expo.: log(base x) (5) = 10
x^10 = 5
(x - a)^2
x^2 - 2ax + a^2
Difference of Squares (x - a) (x + a) =
x^2 - a^2
Use the properties of logs to fund the exact value of each expression: log(base 6) 18 - log(base 6) 3 =
{1}
Foil this out and put into complex form (a + bi): (7-3i)(5 + i)
Ans. 38-8i
Log x + log (x+99) = 2
Ans. x = 1, and x = -100.
Solve the equation: 3^x = 243
Ans. x = 5
Solve : y^2 - 8y + 20 = 0
Ans: 4+- 2i
$ 300 invested at 12 % compounded mostly after a period of 1.5 years. Find the amount results (using the compound interest formula on page 469 of your text). Which says A = P (1 + r/n) ^ (nt) where r is the rate in percent to be converted into decimal, and n is the times it is compounded per year (monthly means 12 times a year).
Ans: A = 300 (1 + .12/12)^12(1.5) = 358.84.
Given f(x) = 2x and g(x) = 5x^2 + 7; find f(g)(4), and g(f)(2)
Ans: a) 174, b) 87
If you want to have $ 1000 in 9 months, how much do you need to place in your savings account now that pays 5 % compounded quarterly?
Answer: $ 963.42
Use the calculator to express the following (round your answer to nearest three decimal places). e^3 + 2 =
Answer: 22.086 This was found by e^3 = 20.0855 + 2 = 22.086
Find the inverse function to the following: 6x/(x+2)
Answer: 2x / (6-x)
True/False To graph y = (x - 2)^3, it shifts the graph of y = x^3 to the left 2 units
Answer: False (look to page 247-256 for reasons)
Determine whether the function is one to one: y = sort(x +3) - 5 .
Answer: Yes. This can be shown first finding the inverse: f^-1 = (x + 5)^2 - 3; Then finding the composite of f(g) = g(f) = x, then you know the function is one to one.
Solve the following equation: 8 - 2e^(-x) = 4
Answer: x = - ln (2) = - 0.693
Solve: ln e^(-2x) = 8
Answer: {-4}
Solve the exponential equation: 3^x = 14
Answer: {ln(14)/ln(3) = 2.402
If $ 1000 is invested at 5 % compounded monthly. How much is there after 8 months?
Using the interest formula {A = P (1 + r/n)^nt} where n = 8, and r = .05, we should get 1033.82 (rounded to nearest 100th). {A = 1000(1+ .05/12)^12(2/3) = 1033.82
Use the given function ( 1 - log(b5) (x -2 ) ); find the following: a) domain, b) Range, c) what are asymptotes if any), d) inverse, e) the inverses domain.
a) {x | x > 2 } b) {y | all real} c) VA: x = 2 d) f^-1 = 5 ^(1 - x) + 2 d) {All real} e) {y| y > 2}
f(X) = sqrt. (3x) , and g(x) = 1 + x + x^2, find f composite g
ans: sqrt. of (3 + 3x + 3x^2); domain is all real.
4b - 10 >= 12 + 2b (Solve this inequality)
b>= 11.