Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

composite functions

I've always learnt that for a composite function:

The following rule applies:

However, this doesn't apply to a function such as :

For which I have worked out the domain of the composition to be

How can this be explained?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: composite functions

You're doing g first, then f, so the range of g must fit within the domain of f.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: composite functions

That’s because of the domain of

must also be a subset of the range of

. The range of

is

, but

is only defined for

. Hence the domain of

is only the set of those values of

in the domain of

for which

is in the domain of

.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: composite functions

Me too slow.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: composite functions

Thankyou!