Question

The function T = F(H) estimates the temperature (degrees Celsius) on a mountain given the height (in meters) above sea level. Use this function: T = 50 - H/20.

Answer 1

1. What is F(500)? What does F(500) mean?
2. Find H in terms of T. Label this function G.
3. What is G(25)? What does G(25) mean?
4. Are the functions F and G inverses of each
other? Explain.

Answer 2

My Answers:

1. 25; At a height of 500 feet above sea level, the temp would be 25 degrees Celsius
2. G(T) = 1000 - 20T
3. 500; At a height of 500m above sea level, the temp is 25 degrees Celsius
4. I need help on.

Answer 3

@AravindG

Answer 4

For number 1: The unit should be [m]. :)
Number 2 is alright. :)
Number 3 is also alright, but it may be restated as "The temperature of 25 degrees C is attained at 500 [m] above sea level." to match the way function G is defined. :)
For number 4: F is one-to-one, that is, given a value of T, there exists one and only one value of F(T). Therefore F has an inverse, and that inverse is precisely given by G. To check it you need to show that \((F \circ G)(T)=T\) and \((G \circ F)(T) = T.\) I will only show the first one.

Let \(F(H)=50-\frac{H}{20}\) and \(G(T)=1000-20T\). Then
\[(F\circ G)(T) = F(G(T))=F(1000-20T)=50-\frac{1000-20T}{20}=50-50+T=T\]