Question

find inverse of the function:::
y=x^3+3x+1

Answer 1

@RadEn @goformit100 can u guys help me?

Answer 2

f^-1(x) = 2^(1/3)/[√(x^2 + 2x + 5) - x - 1]^(1/3) - [√(x^2 + 2x + 5) - x - 1]^(1/3)/2^(1/3)

Answer 3

how did u get that @cutepochacco ? used wolfram didnt u?

Answer 4

what you want to do in inverse problems.. if it is y = x something... replace y by x and solve for y. you can do it the other way and sub variables at the end... i always found it easier to just substitute up front and solve for the variable.

Answer 5

um @Nameless actually i am used to the process of finding the inverse by taking y. but this is a cubic equation so i am not being able to sepate the x and y. let alone substitution at last....

Answer 6

http://www.purplemath.com/modules/invrsfcn3.htm Might help :)

Answer 7

@PayPay777 when i google search thats the first result shown but its of no help....
i tell u i know the method of finding inverse but it cannot be applied here.

Answer 8

you are not separating.. just switching around x and y and solving for y. so it will be x=y^3+3y+1. then solve for y.

Answer 9

basically you will end up with a lot of cubed roots in a rational function. it is kinda nasty in my opinion.

Answer 10

yeah its becoming too complicated.
the main problem is that this function cannot be made up into any sort of a(y+b)^3+c form.

Answer 11

as a result its very hard to sove for y.

Answer 12

@Nameless

Answer 13

i agree.. this one is nasty. a good homework problem... terrible test question. perhaps there is an easier way... but I have not really tried extensively as I am also doing hw

Answer 14

yeah this was a test question

Answer 15

actually the question was :
find the area enclosed by f(x), x=1, x=15, where f(x) is the inverse of the given function. @Nameless !!!!!!!!!

Answer 16

the given function is the one on the top?

Answer 17

yeah

Answer 18

and bounded by the x axis on the bottom?

Answer 19

not given in question

Answer 20

can you paste the question? are you using calculus to find area? or Algebra?

Answer 21

calculus of course

Answer 22

area enclosed by y=f(x), x=1,x=15 where f(x) is inverse of g(x)=x^3+3x+1 is

a 9/4 b. 18
c 3/4 d. none of these

Answer 23

dont say none of these @Nameless lol hahaha

Answer 24

Here is the inverse generated by Mathematica
\[
\frac{\sqrt[3]{\sqrt{x^2-2
x+5}+x-1}}{\sqrt[3]{2}}-\frac{\sqrt[3]{2}}{\sqrt[3]{\sqrt{x^2-2
x+5}+x-1}}
\]

Answer 25

i know that @eliassaab but i cant figure out how to do it.

Answer 26

I think it involves finding roots of cubic using formulas similar to the quadratic formula

Answer 27

http://en.wikipedia.org/wiki/Cubic_function

Answer 28

u may use symmetry to avoid finding the inverse

Answer 29

find the area enclosed by f(x), x=1, x=15, where f(x) is the inverse of the given function.

if u think bit hard you can set up the area integral as below :-
2*15 - [ int 0->2 (x^3+3x+1) dx ]

Answer 30

Agree with @ganeshie8 and the answer is 18

Answer 31

yeah ans is 18

Answer 32

but why 2*15 i didnt get that!!

Answer 33

@ganeshie8 please explain!

Answer 34

first observation : area between f and y axis = area between inverse(f) and x axis

Answer 35

okay

Answer 36

area between f and y axis in interval y = [1, 15] :
int 1 to 15 x(y) dy

which is same as :

2*15 - int 0 to 2 y(x)dx

Answer 37

let me try to show u in graph, it becomes easy to convince :)

Answer 38

sure :)

Answer 39

those two green areas area same, from our first observation of symmetry.

Answer 40

next we wanto figure out how to compute the area between y = f(x) and y-axis
(vertical green region)

Answer 41

area of vertical green region = (area of rectangle of 2x15) - (area below y=f(x) in that region)

Answer 42

green + blue = 2*15

blue = 2*15 - blue

Answer 43

thanks @ganeshie8 100 medals to u!!! :)