Help with inverse function (1 Viewer)

[hon1hon2hon3]

hey guys , i have already forgotten all my 3 unit stuff right after my HSC , and now i could do a 3unit maths question . . a little help thx

i) Show that f(x) = x^3 - 2x^2 +2x +5 , considered as a function defined fo all x , has an inverse function g(x) (Do not attempt to find a formula fo the inverse function)


ii) Sketch the graph of f(x) and g(x) on the same diagram

Thankyou

 

[alakazimmy]

f'(x) = 3x² - 4x + 2

Discriminant = 16 - 24 < 0
Hence, no real roots exist for f'(x). So f'(x) > 0 for all values of x

Therefore, f(x) is always an increasing function, so it is a one-to-one function.

 

[Drongoski]

i)

f'(x) = 3x^2 - 4x + 2 = after some fiddling = 3(x - 2/3)^2 + 2/3 >= 2/3 > 0

i.e. f(x) is strictly monotone (increasing in this case) for all x and therefore has an inverse

 

[hon1hon2hon3]

This must sounds strange , u doing commerce and law in unsw ? commerce majoring in actuarial ? And u are tutoring people ? Cuz i need help in both actuarial and law lol , if u are a tutor how much do u charge ???

 

[alakazimmy]

Sorry, I'm not capable of doing individual tutoring for any uni courses yet. Maybe wait one or two years .

I'm assuming you are doing MATH1151 this semester.
I take a support class for this course on Tuesdays 10-11 every week. Feel free to come along.
The other support classes, I think are on Monday 12-1 and Friday, sometime.

Check the asoc (Actuarial society) website to verify these times - (google unsw asoc)

Also, come to the poker night next Tuesday 6pm start =P