Find Composite Function Components

• Jan 20th 2007, 05:53 AM
symmetry
Find Composite Function Components
Find functions f and g such that f (g) = H if H (x) = 1/(x + 1).
• Jan 20th 2007, 09:21 AM
CaptainBlack
Quote:

Originally Posted by symmetry
Find functions f and g such that f (g) = H if H (x) = 1/(x + 1).

Suppose f(x)=1/x, and g(x)=x+1, then:

f(g(x))=f(x+1)

then if y=x+1, we have f(g(x))=f(y)=1/y=1/(x+1),

so H(x)=1/(1+x), as required.

RonL
• Jan 20th 2007, 12:53 PM
symmetry
ok
Very impressive, Ron.

Tell me, is finding composite function components required in calculus?
• Jan 20th 2007, 01:42 PM
CaptainBlack
Quote:

Originally Posted by symmetry
Very impressive, Ron.

Tell me, is finding composite function components required in calculus?

I don't know I have never followed the US maths course sequence (we
don't/didn't do things that way in the UK). As far as I recall we learned
stuff as it was needed.

Some knowledge of composite functions is needed for the chain rule, but
as far as I recall a formal treatment of composite functions was not needed
in the courses I pursued until the transition to university real analysis (1st