Part 1 find the composite function Find g composite f Explai

Part 1, find the composite function.

Find g composite f. Explain why f composite g is undefined.

Part 2. In school, Jack and Sam exchanged notes in a code f which consists of spelling every word backwards and interchanging every letter s with t. Alternatively, they use a code g which interchanges the letters a with o, i with u, e with y, and s with t. Describe the codes f composite g and g composite f. Are they the same?

Give f composite g and g composite f in the same tabular form.

These are Abstract Algebra Problems.

Solution

1) f(x) = 1/x

g(x) = ln x

g composite f = (gof)(x) = plug f(x) into g(x)

(gof)(x) = ln ( 1/x )

f composite g = (fog)(x) = plug g(x) into f(x)

(fog)(x) = 1 / ln x

f composite g is undefined since division by ln 0 is undefined