Math Is Fun Forum

Ridley-C

Member

Registered: 2015-07-31

Posts: 4

Functions help!!!!!!!!!!!!

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$).

If the graphs of $y=f(x^2)$ and $y=f(x^4)$ are drawn, at how many points do they intersect?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Functions help!!!!!!!!!!!!

hi Ridley-C

I thought I'd collect some data by choosing various functions:

(1)  If f(x) = x, then the two graphs only intersect at the origin.

(2) If f(x) = 2x+ 1, there are three points of intersection.

(3)  If f(x) = sin(x) then strictly it isn't invertible, but if you limit to [0,pi/2] then there are 5.

That's as far as I've got so far.  Did you expect a single answer for all f(x) ?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Ridley-C

Member

Registered: 2015-07-31

Posts: 4

Re: Functions help!!!!!!!!!!!!

Oops I'm stupid xD