F(f^-1) = x

1. Feb 7, 2006

teng125

can anybody pls give me an example of this f(f^-1) = x??
thanx.......

2. Feb 7, 2006

abszero

It's the definition of the inverse of a function f(x). For example, y = 2x and y^-1 = 1/2 x

3. Feb 7, 2006

teng125

how about if i want to write it using sin x??

4. Feb 7, 2006

HallsofIvy

Staff Emeritus
Although I would say f(f-1(x))= x. You're missing the "x" on the left side!

"arcsine" is defined as the inverse of sine (that's why your calculator has them paired). sin(arcsin(x))= x.

There are "technical" problems. Since sin(x) is not "one-to-one" ($sin(\pi)= 0= sin(0)$) there can't be a true inverse (a function can't return both 0 and $\pi$ for x= 0). What is normally done is restrict the sine function to x=0 to $\pi$ (which is really a different function than sine defined for all x) so that arcsin returns the "principal value"- the value between 0 and $\pi$.

5. Feb 8, 2006

VietDao29

We don't really restrict sin function to x = 0 to $\pi$.
We, however, restrict sin function to $$x = -\frac{\pi}{2}$$ to $$x = \frac{\pi}{2}$$. :)

6. Feb 8, 2006

HallsofIvy

Staff Emeritus
Oops! It's cosine that is restricted to "between 0 and $\pi$!