I have this homework problem that I'm having trouble with. It is:
If f(x) = 1 - x3 and f-1 is the inverse of f, how many solutions does the equation f(x) = f-1 have?
I did the inverse as such:
x = 3√(1-x)
It looks to me as if they equal each other twice but that is not a choice. :( The choices are:
A. 0
B. 1
C. 3
D. 5
E. 6
If you graph both equations, you'll find 5 intersections. Where there's intersections, that shows the two equations are equal with those X values.
Thus, D is the answer.
Edit: I wrongly corrected you. Hope it isn't too late to make the correction. I just realized it today when I was thinking about it again. The error was just my wrong method of finding a function's inverse. :-\
I graphed it on my TI87 and used ZBox around the intersection. It is D.
So how is your answer wrong?
y = 1 - x3
x = 1 - y3
1 - x = y3
3√(1 - x) = y
Quote from: Shout on January 05, 2006, 09:47 PM
I graphed it on my TI87 and used ZBox around the intersection. It is D.
So how is your answer wrong?
y = 1 - x3
x = 1 - y3
1 - x = y3
3√(1 - x) = y
I had a correction on your answer that was wrong because I didn't use the correct method for finding an inverse. I just deleted that bit of my post to avoid confusion.
I don't think it can be solved easily without graphing.
Mathematica:
Plot[{1 - x^3, (1 - x)^(1/3), -(x - 1)^(1/3)}, {x, -1, 1.5}]