inv functions question from 2004 3U HSC paper (1 Viewer)

[gamja]

Q5b of the above hsc paper:
- The graphs of y=f(x) [ for x>=0] and y=invf(x) [which I calculated to be ]meet at exactly one point P. Let α be the x-coordinate of P. Explain why α is a root of the equation

x^3 +x -1 = 0.

​

I let both function formulae equal each other and squared them and eventually came out with a long 5-th degree polynomial. Any ideas? (much appreciated

 

[Nedom]

Don't equations and their inverse intercept at y=x. (I don't even know if that's relevant, just something to consider). Then you could just find the root of the equation. Then equate, huzzah.

 

[Nedom]

Wait lmao, it's so ez. I am so stupid. If you equate the f(x) and y =x, you rearrange you get the equation, and that gives the answer. LMAO, too rusty at maths.
(So same thing as I said before, but you don't need to solve for the root of the equation, it's unneccessary)
(Didn't actually try it so my first response is half-assed, don't worry about that one)

 

[gamja]

Wait lmao, it's so ez. I am so stupid. If you equate the f(x) and y =x, you rearrange you get the equation, and that gives the answer. LMAO, too rusty at maths.
(So same thing as I said before, but you don't need to solve for the root of the equation, it's unneccessary)
(Didn't actually try it so my first response is half-assed, don't worry about that one)

very true [highkey embarrassing that i forgot the y=x rule omg] thank you

 

[Average Boreduser]

Q5b of the above hsc paper:
- The graphs of y=f(x) [View attachment 37328 for x>=0] and y=invf(x) [which I calculated to be View attachment 37329]meet at exactly one point P. Let α be the x-coordinate of P. Explain why α is a root of the equation

x^3 +x -1 = 0.

​

I let both function formulae equal each other and squared them and eventually came out with a long 5-th degree polynomial. Any ideas? (much appreciated

Bro why u doing 2004 3u questions lmfao that literally 2 decades old

 

[5uckerberg]

Bro why u doing 2004 3u questions lmfao that literally 2 decades old

When will people ever learn that some of the old questions are still related to the new syllabus like inverse functions.

 

[gamja]

Bro why u doing 2004 3u questions lmfao that literally 2 decades old

just going thru 3u revision across entire syllabus starting from FWWF lol probably the last opportunity i have to do that as well

 

[Trebla]

Bro why u doing 2004 3u questions lmfao that literally 2 decades old

FYI the 2022 Maths Ext2 HSC had a question that was almost identical to one in the 2005 Maths Ext2 HSC. Just sayin…

 

[Average Boreduser]

LMFAO fr?

 

[yanujw]

LMFAO fr?

Yep. There was even a discussion about it on the ext 2 hsc thoughts thread. You can absolutely use past HSC exams from previous syllabi, just make sure the content is related to the new syllabus.