Some help with inverse function thx ~~ (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 do know this is a 4unit forum, but i am posting here looking for some smart ones for a quick reply , forgive me i got a test tommorow lol )

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

 

[lolokay]

the derivative of the function is
3x² - 4x + 2
= 3(x - 2/3)² + 2/3 > 0 for all x
graph is monotonic increasing .'. an inverse exists

to sketch just find intercepts, point of inflexion etc.

edit: question was already answered in other thread

 

[Timothy.Siu]

f'(x)=3(x-2/3)^2+14/9

nope

 

[shaon0]

nope

lol. i thought i deleted the post u replied to sorry.