Composite functions

Just started uni, haven’t done any maths for over 3 years so apologise if this is an easy question. I’ve done the first bits and sketched y=f(x) and y=g(x), I’m just not sure how to go about sketching y=f(g(x)) or y=g(f(x)). Any help appreciated

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Reply 1

mqb2766

Original post by kwikmaffs

Id probably split f up into the regions where its "easy" so x<0, 0<x<1, x>1 and for f(g(x)) say reason about what happens to g in each case so a reflection, identity, constant. If necessary, just trace a few (critical) points through and think what happens between them.

(edited 6 months ago)

Reply 2

tonyiptony

For the most part there is no trick to graphing composite functions, you kind of just need to figure out what happens in each interval of interest (which can be tricky).

Usually though, I would first figure out what f(g(x)) really is. That's where sketching f(x) and g(x) separately can help.