Function Operations
Given the functions f and g, perform the indicated operations. f(x) = 2x + 3, g(x) = 8x - 7. Find fg.
16x2 + 10x - 21
A coin is tossed and a die is rolled. Find the probability of getting a head and a number greater than 2.
1/3
During the development stage of a new rectangular keypad for a security system, it was decided that the area of the rectangle should be 221 square centimeters and the perimeter should be 60 centimeters. Find the dimensions of the keypad.
13, 17
Simplify:
i^(2)
-1
Given the terms 3, 7, 11,...
Is the sequence arithmetic or geometric?
What is the common difference or common ratio?
d = 4
2x^2 + 49 = 0
x=7i,-7i
A jar contains four blue marbles and three red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event.
Both of the selected marbles are red. (Round to 3 decimal places.)
0.143
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula E=IR. Solve the problem using this formula. Find E, the voltage of a circuit, if I = (9 + 2i) amperes and R = (4 + 6i) ohms.
24 + 62i
Simplify:
(1+2i)-(4+2i)
-3
Find the 4th term of the sequence 5, -20, 80,...
-320
Let f(x) = x2 - 6 and g(x) = 19 - x, Find (fg)(5)
266
Find the horizontal asymptote: f(x) = (-8x + 7)/(5x + 2)
y = -8/5
For the given exponential function, find the average rate for x = 3 and x = 7. f(x) = ex-3 - 7. Round the the hundredths.
13.40
Simplify
(3+2i)^2
5+12i
Find the 27th term of the sequence. 24, 21, 18, ...
-54
If f(x) = 5x - 8 and g(x) = x - 8, find (f o g)(x)
Find the relative maximum and relative minimum of the graph: f(x) = x3 +3x2 -3x. Round to the hundredths.
Max: (-2.41, 10.66)
Min: (0.41, - .66)
The profit that the vendor makes per day by selling x pretzels is given by the function p(x) = -4x2 + 2800x - 150. Find the number of pretzels that must be sold to maximize profit.
350 pretzels
Simplify
(8 + 3i)(6 + i)
45 + 26i
If the 4th term of a geometric progression is -16/3 adn the 5th term is 32/3, find a1 and r
a1 = 2/3
r = -2
Solve: Let f(x) = x + 3 and g(x) = x2. Find (g o f)(3)
36
**Open google slides**
This problem involves empirical probability. The table shows the breakdown of 89 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest hundredths.
0.3
Find the average rate of change of the function, f(x) = log46x on the interval x = 4 to x = 9. Round to the thousandth place.
0.117
Find all the zeros of the function: g(x) = x3 + 20x2 + 68x + 289
-17, -3 +/- i sqrt 59 over 2
Jose takes a job that offers a monthly starting salary of $3500 and guarantees him a monthly raise of $130 during his first year of training. Find the general term of this arithmetic sequence and his monthly salary at the end of his training.
3500 + 130(n-1)
4930