Question

The function C(t) below relates outside temperature in degrees Fahrenheit to the number of cricket chirps per minute.

It takes as input the temperature in degrees Fahrenheit, and returns as output the number of cricket chirps per minute occurring at that time.

C(t) = 5t - 200

Which equation below represents the inverse function T(c), which takes the cricket chirps per minute as input and returns as output the temperature in degrees Fahrenheit?
a) T(c) = (c+5) / 200
b) T(c) = (c-5) / 200
c) T(c) = (c-200) / 5
d) T(c) = (c+200) / 5

Answer 1

C(t) = 5t - 200
T = 5t - 200
5t = T + 200
t = (T + 200)/5
T(c) = (T + 200) / 5

Answer 2

Answer: d)
`T(c)=((c+200))/(5)`

Explanation:

Given: The function C(t) relates outside temperature in degrees Fahrenheit to the number of cricket chirps per minute.

`C(t)=5t-200`

To find the inverse function of C(t) [named as T(c), rewrite the above equation as
`c=5t-200\\\Rightarrow5t=c+200\\\Rightarrow\ t=(c+200)/(5)`

Now, replace 't' by T(c), we get

`T(c)=((c+200))/(5)`