# Algebra involving functions

joe shmo
Posers and Puzzles 19 Nov '07 03:17
1. joe shmo
Strange Egg
19 Nov '07 03:171 edit
I have a question this is what I have come up with, here is the problem

an organization determines that the cost per person of chartering a bus is given by the formula

C(x) = (100 + 5x)/x

where x is the number of people in the group and C(x) is a dollar amount

Its asking me to find C-1(x) and explain what it represents, to clear up my notation its asking for the inverse of C(x)

The problem is when I go to fing C-1(x) I come up with

C-1(x) = ( xy - 100)/5

I arrived at this by using the method i was taught replacing C(x) with y and replacing the x's in the original C(x) function with y's to get:

x = (100 + 5y)/y then I am supposed to rearrange for y. this is apparently where i run into problems.

can anyone point out where Im screwing up.

Thank you
2. joe shmo
Strange Egg
19 Nov '07 03:501 edit
Originally posted by joe shmo
I have a question this is what I have come up with, here is the problem

an organization determines that the cost per person of chartering a bus is given by the formula

C(x) = (100 + 5x)/x

where x is the number of people in the group and C(x) is a dollar amount

Its asking me to find C-1(x) and explain what it represents, to clear up my notation i parently where i run into problems.

can anyone point out where Im screwing up.

Thank you
i think I found my error

if I break C(x) = (100 + 5x)/x into C(x)= 100/x + 5x/x

I get C-1(x) = 100/x-5

and composing the functions I get C(C-1(x)) = x which is proof that they are inverse. However, Im still having trouble figuring out what C-1(x) means as far as the charterbus situation
3. joe shmo
Strange Egg
19 Nov '07 04:04
Originally posted by joe shmo
i think I found my error

if I break C(x) = (100 + 5x)/x into C(x)= 100/x + 5x/x

I get C-1(x) = 100/x-5

and composing the functions I get C(C-1(x)) = x which is proof that they are inverse. However, Im still having trouble figuring out what C-1(x) means as far as the charterbus situation
i see there is a domain restriction in C-1(x)Domain: x > 5
because there would be no people chartering the bus i suppose otherwise......could this be it?
4. joe shmo
Strange Egg
19 Nov '07 04:08
Originally posted by joe shmo
I have a question this is what I have come up with, here is the problem

an organization determines that the cost per person of chartering a bus is given by the formula

C(x) = (100 + 5x)/x

where x is the number of people in the group and C(x) is a dollar amount

Its asking me to find C-1(x) and explain what it represents, to clear up my notation i ...[text shortened]... parently where i run into problems.

can anyone point out where Im screwing up.

Thank you
5. AThousandYoung
All My Soldiers...
19 Nov '07 06:12
Originally posted by joe shmo
I have a question this is what I have come up with, here is the problem

an organization determines that the cost per person of chartering a bus is given by the formula

C(x) = (100 + 5x)/x

where x is the number of people in the group and C(x) is a dollar amount

Its asking me to find C-1(x) and explain what it represents, to clear up my notation i ...[text shortened]... parently where i run into problems.

can anyone point out where Im screwing up.

Thank you
y = (100+5x)/x

xy = 100+5x

xy - 5x = 100

x(y-5) = 100

x = 100/(y-5)
6. 19 Nov '07 10:09
Originally posted by joe shmo
However, Im still having trouble figuring out what C-1(x) means as far as the charterbus situation
What it means: the inverse function will give you the number of people in the group given the cost.