## find formula for inverse: f,g,h invertible, f(x)=g(h(x))

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### find formula for inverse: f,g,h invertible, f(x)=g(h(x))

Suppose f, g, and h are invertible and that f(x)=g(h(x))
I need to find a formula for f-1(x) in trems of g-1 and h-1
so, I was thinking that inverse of f(x) would be h(g(x)), but when it asks for g-1 and h-1, there's a step I'm missing. How do I look for g-1?
santaclaus

Posts: 41
Joined: Tue Mar 03, 2009 12:17 am

santaclaus wrote:Suppose f, g, and h are invertible and that f(x)=g(h(x))
I need to find a formula for f-1(x) in trems of g-1 and h-1
so, I was thinking that inverse of f(x) would be h(g(x))...

How did you arrive at this conclusion...?

To learn about inverse functions, try here. Once you have learned the basic terms and techniques, note that you would be solving "y = g(h(x))" for "x=":

. . . . .$y\, =\, g(h(x))$

. . . . .$g^{-1}(y)\, =\, h(x)$

. . . . .$h^{-1}\left(g^{-1}(y)\right)\, =\, x$

And so forth.

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm