Lori has determined a function f(x) that shows the exponential growth of the number of jeans Tim owns each year. Explain how the f-1(x) can be found and what f-1(250) means.

Question

ashleyisakitty · Answer

Are you looking for the inverse or the derivative?

anonymous · Answer

The inverse, I'm sorry

anonymous · Answer

@Ashleyisakitty

ashleyisakitty · Answer

To find an inverse, you switch around the variables in an equation. For example, if you had y=6x+2, and you wanted to find the inverse, you would make the equation x=6y+2, and then solve for y, ending up with an answer of y=(x-2)/6. That answer is the inverse equation, and to find the inverse of a value, like f-1(250), you just plug in 250 as the x-value. f(250) is the number of jeans tim owns at the 250th of whatever time interval is being used. An interval gives the opposite value of the original function, so the f-1(250) gives you the time when f(x)=250, aka when tim has 250 jeans.

anonymous · Answer

Okay I gotcha, well since this equation didn't really give me any numbers I just made the equaton y=2^x. How would I find that inverse? @Ashleyisakitty

ashleyisakitty · Answer

You switch around the variables. So, y=2^x becomes x=2^y. However, by choosing this equation, you've made things harder for yourself, as you have to take the log of both sides to solve. I would suggest using y=x^2. If you want to solve that one, take the log of both sides, giving you log(x)=log(2^y). Exponents in logs can become multipliers of the log, so it becomes log(x)=ylog(2). Then, you simplify, and get y=(logx)/(log2).

anonymous · Answer

okay, thanks!

anonymous · Answer

and hypothetically i switched it to the y = x^2, and turned it inverse. so f^-1(250) = y^2. 250 would subsititute for x? @ashleyisakitty

anonymous · Answer

@Ashleyisakitty