Please help me with inverse functions!!!!!!!!!!

Question

wikiemol · Answer

all you have to do when finding the inverse function is 
1. switch x and y 
2. solve for y in terms of x.

anonymous · Answer

but its a word problem

wikiemol · Answer

What is the word problem?

anonymous · Answer

The weight w(in pounds) that can be supported by a shelf 
made from half-inch Douglas ﬁr plywood 
 can be modeled by w=(82.9/d)^3
 where d is the distance (in inches) between the 
supports for the shelf. Find the inverse of the model.

wikiemol · Answer

the inverse of the model would then be d=(82.9/w)^3

anonymous · Answer

REALLY!!!!!!!!?

wikiemol · Answer

yes, I am pretty sure. The inverse of a function in mathematical terms simply involves switching two variables. In other words if f(x) = g(x) then the inverse is g(f(x)).

anonymous · Answer

Oh my goodness thank you so much i was legit trying to find the cubic root of w and a whole bunch of other stuff

wikiemol · Answer

well yeah, more explicitly you might want to solve for w, so the inverse function would be:

$$\sqrt[3]{d} = 82.9/w$$

$$\frac{ 82.9 }{ \sqrt[3]{d} } = w$$

but the inverse of the model would simply involve switching the variables. The difference is a model just describes the relationship between two variables, a function is an operation on a variable which takes one parameter.

anonymous · Answer

Oh for w all i have to do is plug in 84 and BAM! The answer is there

wikiemol · Answer

im not sure where you got the 84 from haha, im guessing that is another part of the problem?

anonymous · Answer

yes there is another part i just needed help with the equation, once again THANK YOU!

wikiemol · Answer

No problem!