Question

I need help with finding the inverse of this function, 2x^5+x^3+1.

Answer 1

\[2x^5+x^3+1\]

Answer 2

hmm, technically, the inverse is just swapping about the variables, now the simplification, well, not so simplistic

Answer 3

exactly, I know the concept it's just that I have to show my work to simplify and insert a value into the new function.

Answer 4

Interesting...
Can somebody find the inverse function for \(y=x^2+2x-3\) ?

Answer 5

yes... but you will have to restrict the domain.

Answer 6

Two branches will satisfy:
\[-1\pm\sqrt{4+x}.\]Now how to solve this one?
\[2y^5+y^3+1-x=0.\]

Answer 7

throwing it into wolframalpha gives this result
http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427ef49hilhcgk

Answer 8

This means that the inverse function may not be found.

Answer 9

whaaaaaat...... But It's in my textbook and part of my homework! Ugh...

Answer 10

what are you studying?

Answer 11

calc one... this is the second day of homework.

Answer 12

you sure it's a 5th power?

Answer 13

sorry, that's the class. I'm studying Electrical Engineering. just a second and I'll upload a snapshot of the problem

Answer 14

#74

Answer 15

Hahaha. Lol.

Answer 16

hmm well well

Answer 17

dude... it says f^-1(a) and gives you the value of a.

inverse functions work like this...
plug in the y from a function into its inverse and you get out x.

compute f(a) for your functions and then f^-1(f(a)) will just be a.

Answer 18

I know, and I have the -71 as the answer, but it also asks to write down the function which I can't find to save my life!

Answer 19

oops... i misread. but i doesn't ask for the inverse function... only f^-1(a)

Answer 20

OH! oh oh oh oh.... Damn....

Answer 21

if you find a = f(x) then the x that satisfies this will be f^-1(a)

Answer 22

Wow that's a lot easier than finding \(f^{-1}(x)\) :)

Answer 23

yeah, it's -71...

Answer 24

craaaaap.... well there went an hour I'll never get back. thanks for all your help guys

Answer 25

no worries... maybe post the question from your book and your interpretation so you can get to the heart of the sunrise quicker.

Answer 26

So, what is an answer?

Answer 27

it's not -71

Answer 28

no?

Answer 29

x = -1

-2 = 2x^5 + x^3 +1 => 2x^5 + x^3 +3 = 0

the only real solution is x = -1

Answer 30

yeah I get what you mean now... but isn't that just f(-2) now? not the inverse?

Answer 31

no... f(-1) = -2 so

f^-1(-2) = -1

Answer 32

Remember that \(f^{-1}(-2)\) is that domain element x that gives you \(f(x)=-2\)

The function maps the domain to the range.

The inverse function maps the range back to the domain.

Answer 33

Let \(f^{-1}(a)=x\). Now map \(f\) to both of the parts of the equation and use \(f(f^{-1}(a))=a\). It will become\[a=f(x)\]Solve this and you will obtain an answer.

Answer 34

So by setting \(f(x)=y=-2\) and solving, you find the x in the domain that takes you to y in the range.

Answer 35

f^-1(f(x)) = x

Answer 36

ohhh okay, so put the variable as the solution and work backwards

Answer 37

they give you a = f(x) and want you to find f^-1(a) = f^-1(f(x)) = x

so setting f(x) = a and solving for x gives you what you need.

Answer 38

make sense?

Answer 39

Yep :) thanks again y'all

Answer 40

you're welcome!

Answer 41

*lightbulb turns on* I think the rest of this will be much easier now

Answer 42

awesome! let's turn the dark into light!