The Purplemath Forums

by **santaclaus** on Mon Apr 13, 2009 7:14 am

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? :confused:

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by **stapel_eliz** on Mon Apr 13, 2009 10:55 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. :wink:

The Purplemath Forums

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

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