Expert: Paul Klarreich - 1/13/2008

Question
hi. i have tried doing these three problems, but i cannot seem to get the answer. i would appreciate it if you could help me. thanks!

1) determine the domain of the function. 6x/x(x^2-16)

2) find the inverse of the function.  2x+1/3

3) 4x/x(x^2-36)

Answer
Questioner:   kacey
Category:  Calculus
Private:  No
 
Subject:  pre-cal
Question:  hi. i have tried doing these three problems, but i cannot seem to get the answer. i would appreciate it if you could help me. thanks!

1) determine the domain of the function. 6x/x(x^2-16)

2) find the inverse of the function.  2x+1/3

3) 4x/x(x^2-36)
.......................................
Hi, Kacey,

1) determine the domain of the function. 6x/x(x^2-16)

The domain of a function written like this is 'all x for which there is no boo-boo.'

A boo-boo would be (in this case) a division by zero.

That happens here if  x = 0 or x = +- 4.  So your domain is:

all x /= 0,4,-4.   [/= says 'not equal'.]


2) find the inverse of the function.  2x+1/3

To find an inverse,

1. Write  y = f(x)
2. Exchange x and y.
3. Solve for y.

y = 2x + 1/3
x = 2y + 1/3

x - 1/3 = 2y

y = x/2 - 1/6

That's your inverse.


3) 4x/x(x^2-36)
HUh?  What do you do here?