Please help with this one question? I honestly suck at inverses and don't even know where to start.
Show work too so I can learn for the test! Thanks so much.
1.The rate at which
crickets chirp is a function of the temperature
of the air around them. Suppose that the
following data have been measured for y
chirps (c) per minute at temperatures of x in
degrees Fahrenheit.
x (°F) y (c/min)
20 0
30 0
40 5
50 30
60 55
70 80
80 105
a. Let y = c(x). Find c(40), c(50), and c(60).
b. For temperatures of 40°F and above, the
chirping rate seems to be a one-to-one
function of time. How does this fact imply
that function c is invertible for x ≥ 40? Find
the values of c −1(30) and c−1(80). How do
these values differ in meaning from c(30)
and c(80)?
c. Why is function c not invertible for x in the
whole interval given, 20 ≤ x ≤ 80? What do
you suppose is true in this real-world
situation that makes c not invertible?
d. On graph paper, plot the seven given points
for function c and the corresponding points
for the inverse relation. Connect each set of
points with a line or a smooth curve. Draw
the line y = x and tell how the two graphs
are related to this line. (Just how would I do this problem?)
e. What is the difference in the meaning of x
as an input for function c and x as an input
for function c−1?
Show work too so I can learn for the test! Thanks so much.
1.The rate at which
crickets chirp is a function of the temperature
of the air around them. Suppose that the
following data have been measured for y
chirps (c) per minute at temperatures of x in
degrees Fahrenheit.
x (°F) y (c/min)
20 0
30 0
40 5
50 30
60 55
70 80
80 105
a. Let y = c(x). Find c(40), c(50), and c(60).
b. For temperatures of 40°F and above, the
chirping rate seems to be a one-to-one
function of time. How does this fact imply
that function c is invertible for x ≥ 40? Find
the values of c −1(30) and c−1(80). How do
these values differ in meaning from c(30)
and c(80)?
c. Why is function c not invertible for x in the
whole interval given, 20 ≤ x ≤ 80? What do
you suppose is true in this real-world
situation that makes c not invertible?
d. On graph paper, plot the seven given points
for function c and the corresponding points
for the inverse relation. Connect each set of
points with a line or a smooth curve. Draw
the line y = x and tell how the two graphs
are related to this line. (Just how would I do this problem?)
e. What is the difference in the meaning of x
as an input for function c and x as an input
for function c−1?
-
a. That just asks what y value (column 2) occurs when column 1 says 40, 50 or 60. Just read down column 1.
b. Now read down column 2 and find out which x value occurs when y is 30 and 80. What does the y value corresponding to x = 30 mean? What does the x value corresponding to y = 30 mean?
c. A function is invertible if you can identify which x value goes with a particular y value. What x value goes with y = 0? Can you answer that?
d. I'm going to assume you know how to draw a graph.
e. What's the difference between column1 and column 2?
b. Now read down column 2 and find out which x value occurs when y is 30 and 80. What does the y value corresponding to x = 30 mean? What does the x value corresponding to y = 30 mean?
c. A function is invertible if you can identify which x value goes with a particular y value. What x value goes with y = 0? Can you answer that?
d. I'm going to assume you know how to draw a graph.
e. What's the difference between column1 and column 2?