Question

Solving Inverse Functions:
Evaluate http://prntscr.com/15e7ec Unsure how to solve inverse functions :(

Answer 1

@primeralph over here

Answer 2

do you know calculus?

Answer 3

Yeah. I do.

Answer 4

is this a topic under calc?

Answer 5

ever heard of Lagrange inversion theorem?

Answer 6

i know the equation is \[(f ^{-1})'(a)=\frac{ 1 }{ f'(f ^{-1}(a)) }\] and that in order to solve it, I need the derivative, which is \[f(x) = \sqrt{x^3+x^2+ x+ 1} \rightarrow f'(x)= \frac{ (3x^2+2x+1) }{ 2\sqrt{x^3+x^2+x+1} }\]

Answer 7

But im not sure what to look for after...

Answer 8

chill

Answer 9

you are not looking for the inverse function

Answer 10

you are looking for the derivative of the inverse at \(x=2\)

Answer 11

@satellite73 I've been thinking of a way to make that easier to state. In my opinion, you can flip the differential

Answer 12

so the first step is to see if you can find \(f^{-1}(2)\)

Answer 13

@satellite73 non-numerically, that might be hard...........

Answer 14

you can do it in your head

Answer 15

\(f(1)=2\) so \(f^{-1}(2)=1\)

Answer 16

To find the inverse at 2, i see which value of x for f(x) gives me 2?

Answer 17

so your real job is now this
find the derivative of \(f\)
evaluate it at 1
take the reciprocal
that is all

Answer 18

@satellite73 I think the person needs a more analytic approach..........without assumptions.............

Answer 19

...........that's the hard part.........maybe Lagrange?

Answer 20

@primeralph heck no!
that is what this problem is all about
understanding and using \[(f ^{-1})'(a)=\frac{ 1 }{ f'(f ^{-1}(a)) }\]

Answer 21

it is meant to be easy
find \(f^{-1}(2)=1\) then find \(\frac{1}{f'(1)}\) finished

Answer 22

@satellite73 crap! it's actually numerical from the start..........missed that kinda

Answer 23

So basically you're working backwards.. you're given an output and you find a value of x that satisfies the value given. Correct?

Answer 24

yes

Answer 25

@Jhannybean yeah, that's the def of an inverse

Answer 26

Oh Okay, that's what I was concerned with. it's not solving the equation that got to me, it was more along the lines of using \[(f ^{-1})(2)\]

Answer 27

@Jhannybean as soon as i saw this
Solving Inverse Functions:
in your question, i knew you were on the wrong path
your job is not to find the inverse function, then find the derivative of the inverse etc etc
your job was only to find \(f^{-1}(2)\) and use \[\frac{1}{f'(1)}\]

Answer 28

...I forgot what it meant. And using Stewart's 7th edition calc only tells me the proof of the differential equation.

Answer 29

it is easy once you know the trick
the reason i know this is only because i have seen it repeatedly

Answer 30

it is clear of course that if you could not find \(f^{-1}(2)\) you could not do this problem so fast

Answer 31

I see.Thank you. Oh haha. Its appeared on my practice final exam study guide and i've forgotten how to apply \[f ^{-1}(x)\]

Answer 32

yw