Question

Having a little trouble on a calc II problem. I'm trying to find the inverse of a function like this: f(x)=(2x^2+5x)^(1/2). I started out by finding f'(x), and then (f^1)'(x)=1/f'(x). Now with the slope of the inverse function, I integrated the reciprocal slope for...the wrong answer. Oops. Is this the right approach?

Answer 1

Finding the inverse of a function is a basic calc 1 problem.

Answer 2

Well, it ended up in my Calc II course.

Answer 3

Procedure for finding inverse of a function
Write f(x) as y
Switch x and y
Solve for y
New function acquired is the inverse

Answer 4

Yeah, I tried it that way (algebraically), to. Maybe I'm just making an algebra mistake.

Answer 5

I meant "too".

Answer 6

That's the only way I have seen it in textbooks.. Anyways try again.

Answer 7

The problem is, on a function like this, you can't neatly isolate y.

Answer 8

I kinda saw that. I will try a back of the envelope calculation.

Answer 9

I think you can get there by switching x and y without solving. Differentiating both sides gives dx/dy, which integrated ought to give the inverse...I think.

Answer 10

can someone please help me

Answer 11

Isaiah, I think that's it. I can see a u substitution opening up. Daniella14, I'd recommend starting a new question thread.

Answer 12

can i give you the question here ?

Answer 13

@eighthourlunch

Answer 14

I'd rather you didn't. More people will see it if you add it to the main board, and it won't mess up the one I'm working on.

Answer 15

@eighthourlunch have you tried completing the square first?

Answer 16

Ah, I haven't. I'l try that next, thanks. :)

Answer 17

You can even write as y = ax^2+bx+c as
0= ax^2+bx+(c-y) and then use quadratic formula to solve for x.
Then replace x with f^-1(x) and replace y with x

Answer 18

However you need to take the restrictions of the domain and range of the original function into consideration for choosing the right inverse function

Answer 19

SithsAndGiggles, that was it, thank you! I'd have tried it sooner, but my wife and I were just leaving for our 17th anniversary dinner. I thought it best to prioritize. :) Love your username, btw.
Thanks to everyone else, as well.

Answer 20

You're most welcome!