Converse about the Inverse and Such
y = x
Find the exact value of tan (-pi/3)
- sq rt 3
Without using a calculator or laptop, graph
y = -3x2 + 6
Check against calculator
Name the quadrant -11pi/3 lies in.
Quadrant I
Solve for x.
ex + 1 = 2
ex = 1
x = ln 1
x = 0
Find the inverse function
f(x) = 3x - 2
f-1(x) = (1/3) x + (2/3)
Provide the exact value of the trigonometric function
cos (8pi / 3)
Find the range of the graph of
y = x3 + 5
All Real Numbers
Convert 310 degrees to radians.
31pi/18 radians
Write the following in terms of simpler logarithms:
log(3x4y-7)
10y3 + 4log x + (-7log y)
Find the inverse of
y = 20x + 9
y = ( x - 9) / 20
Find the exact value
sin (5pi/4)
- (sq rt 2) / 2
Find all the points of intersection
x2 + y = 6 and x + y = 4
(-1,5) and (2,2)
Name the reference angle for 2pi/3
pi/3
What is ln e12 ?
12
We have $500 to invest for 37 months. How much money will we have if we put the money into an account that has an annual interest rate of 15% and the interest is compounded quarterly?
$535.84
Find the exact value
cot (5pi)/3
- sq rt 3
Using your brain and no technology, graph
y = (x - 5)2 - 3
Check with calculator.
How many solutions exist for x in
8tan(2x) - 5 = 3 in the interval [-pi/2, 3pi/2] ?
4
{-3pi/8, pi/8, 5pi/8, 9pi/8}
Combine the following into a single logarithm with a coefficient of 1.
3ln(t+5) - 4ln(t) -2ln(s-1)
ln((t+5)3 / t4 (s -1)2)
Let f(x) = 3/x and g(x) = x2 - 1.
Find f(g(x)).
f(g(x)) = 3 / (x2 - 1)
Without using a calculator or laptop, find the solutions within the given interval.
15 = 17 + 4 cos (y/7) in [10pi, 15pi]
No solution!
Find the domain of
f(x) = 1 / (absolute value of (x+3))
All real numbers except -3
How many complete revolutions around the unit circle is the angle
927pi/6 ?
77 complete revolutions
(77.25 revolutions)
Solve 3 + 2 ln ((x/7) + 3) = -4
Round to the nearest thousandth.
-20.789