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22

Step-by-step Answer
PAGE: 389SET: ExercisesPROBLEM: 22
Please look in your text book for this problem Statement

The functions are f equal open curly brackets open parentheses 1 comma 1 close parentheses comma space open parentheses 0 comma minus 3 close parentheses close curly brackets space italic and space straight g equal open curly brackets open parentheses 1 comma 0 close parentheses comma space open parentheses minus 3 comma 1 close parentheses comma space open parentheses 2 comma 1 close parentheses close curly brackets.

To find .

f open square brackets g open parentheses 1 close parentheses close square brackets equal f open parentheses 0 close parentheses space italic or space minus 3               (Substitute g(1) = 0)

f open square brackets g open parentheses minus 3 close parentheses close square brackets equal f open parentheses 1 close parentheses space italic or space 1               (Substitute g(3) = 1)

f open square brackets g open parentheses 2 close parentheses close square brackets equal f open parentheses 1 close parentheses space italic or space 1

f ring operator g equal open curly brackets open parentheses 1 comma minus 3 close parentheses comma space open parentheses minus 3 comma 1 close parentheses comma space open parentheses 2 comma 1 close parentheses close curly brackets

To find g ring operator f.

g open square brackets f open parentheses 1 close parentheses close square brackets equal g open parentheses 1 close parentheses space italic or space 0                    (Substitute f(1) = 1)

g open square brackets f open parentheses 0 close parentheses close square brackets equal g open parentheses minus 3 close parentheses space o r space 1                 (Substitute  f(0) = 3)

g ring operator f equal open curly brackets open parentheses 1 comma 0 close parentheses comma space open parentheses 0 comma 1 close parentheses close curly brackets

f ring operator g equal open curly brackets open parentheses 1 comma minus 3 close parentheses comma space open parentheses minus 3 comma 1 close parentheses comma space open parentheses 2 comma 1 close parentheses close curly brackets and g ring operator f equal open curly brackets open parentheses 1 comma 0 close parentheses comma space open parentheses 0 comma 1 close parentheses close curly brackets.



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