1-6-Assignment-Function-Operations-and-Composition-of-Functions college algebra PDF

Title	1-6-Assignment-Function-Operations-and-Composition-of-Functions college algebra
Author	linli chin
Course	College Algebra
Institution	Lehman College
Pages	8
File Size	352.9 KB
File Type	PDF
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Summary

composition of functions operations involving functions function decomposition...

Description

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 + 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 𝒇 𝒙 = 𝟕𝒙 + 𝟏)( 𝒈 𝒙 = 𝟐𝒙 − 𝟗( ( (

2.(

3.(

𝒇 𝒙 = 𝒙 + 𝟏)( 𝒈 𝒙 = 𝒙 − 𝟒(

4.(

(

(

(

1.( (

(

𝒇 𝒙 = 𝟐𝒙𝟑 + 𝟏)( 𝒈 𝒙 = 𝟐𝒙𝟐 − 𝟏( & & & & & & 𝟕𝒙) ( 𝒇 𝒙 = 𝟐 𝒙) 𝒈 𝒙 = ( 𝟔 ( ( ( ( ( ( (

( Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 − 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 5.( (

7.(

(

𝒇 𝒙 = 𝟓𝒙( 𝒈 𝒙 = 𝟐𝒙 − 𝟏𝟎( ( ( ( ( (

6.(

𝟏 𝒇 𝒙 =𝟒− ( 𝒙 𝟏 𝒈 𝒙 =𝟕+ ( 𝒙 (

8.(

(

(

( ( Copyright © PreCalculusCoach.com

1

𝒇 𝒙 = 𝒙𝟐 + 𝟑𝒙 − 𝟐)( 𝒈 𝒙 = 𝟑𝒙𝟐 + 𝟐𝒙 − 𝟏( & & & & & & & & 𝒙) 𝒇 𝒙 = ( 𝟐 𝒈 𝒙 = 𝒙 − 𝟑( ( ( ( ( ( ( ( ( (

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 ∗ 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 9.( (

𝒇 𝒙 = 𝟔𝒙)( 𝒈 𝒙 = 𝟒𝒙 − 𝟏( (

11.(

𝒇 𝒙 = 𝒙 + 𝟏)( 𝒈 𝒙 = 𝟐 𝒙 − 𝟏(

(

(

Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 13.( (

10.( 𝒇 𝒙 = 𝟓𝒙𝟐 + 𝟐𝒙)( 𝒈 𝒙 = 𝒙𝟑 − 𝟒𝒙 − 𝟏( ( & & & & & & & & 𝒙 + 𝟐) 12.( ( 𝒇 𝒙 = 𝟐 𝒙 − 𝟏) 𝒈 𝒙 = ( 𝟑 ( ( ( ( ( ( ( ( ( ( ( 𝒇 𝒈

𝒙 .(Determine(the(domain(of(each(new(function.(

𝒇 𝒙 = 𝟒𝒙 − 𝟏)( 𝒈 𝒙 = 𝒙 − 𝟒( (

15.(

𝒇 𝒙 = 𝒙𝟐 − 𝟑𝟔( 𝒈 𝒙 = 𝒙 − 𝟔(

(

( ( ( ( ( ( ( (

14.( 𝒇 𝒙 = 𝟐𝒙𝟐 + 𝒙 − 𝟑( 𝒈 𝒙 = 𝒙 − 𝟑( ( & & & & & & 𝒙 + 𝟏) 16.( ( 𝒇 𝒙 = 𝟐 𝒙 − 𝟏) 𝒈 𝒙 = ( 𝟑 ( (

( Copyright © PreCalculusCoach.com

2

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& ( Find(each(composite(function.(Determine(the(domain(of(each(composite(function.( 17.(( 𝒇 𝒙 = 𝒙 + 𝟐)((((((((((𝒈 𝒙 = 𝒙 − 𝟒( 𝒇 ∘ 𝒈 𝒙 =?(((((((((((((𝑫𝒇∘𝒈 =?(

18.( 𝒇 𝒙 = 𝒙 − 𝟏)((((((((((𝒈 𝒙 = 𝒙 𝟐 + 𝟑( 𝒈 ∘ 𝒇 𝒙 =?(((((((((((𝑫𝒈∘𝒇 =?(

(

(&

19.((

&(

𝟏 𝟒 )))))))𝒈 𝒙 = ( 𝒙 𝒙+𝟏 𝒇 ∘ 𝒈 𝒙 =?((((𝑫𝒇∘𝒈 =?(

𝒇 𝒙 =

20.(

( (

&&&&&

(&

( ( ( ( ( ( ( ( ( 𝒙𝟐 )))))))𝒈 𝒙 = 𝒙 − 𝟔( 𝟑 𝒈 ∘ 𝒇 𝒙 =?((((𝑫𝒈∘𝒇 =?(

𝒇 𝒙 = ( ( ( ( ( ( ( ( ( ( (

Find(and(then(evaluate(each(composite(function.( 21.(( 𝒇 𝒙 = 𝟕 − 𝒙))))))𝒈 𝒙 = 𝒙𝟐 − 𝟐𝒙 − 𝟐( 𝒇 ∘ 𝒈 𝟏 =?(

22.(

(

(&

&&&&&&&&&&(

Copyright © PreCalculusCoach.com

3

𝟑) 𝒙 ))))))))𝒈 𝒙 = ( 𝟐 𝒙 𝒈 ∘ 𝒇 𝟑 =?(

𝒇 𝒙 =

( ( ( ( ( ( ( ( ( ( ( ((((

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& ( 23.(( 𝒇 𝒙 = 𝟏 − 𝟐𝒙))))))𝒈 𝒙 = 𝒙 + 𝟏( 𝒇 ∘ 𝒈 −𝟏 =?(

24.(

(

(&

&(

𝟐𝒙 𝒙 − 𝟒) ))))))))𝒈 𝒙 = ( 𝟑 𝟐 𝒈 ∘ 𝒇 −𝟐 =?(

𝒇 𝒙 =

( ( ( ( ( ( ( ( ( ( ((((

( Express)𝒉 𝒙 (as(a(composition(of(two(functions(𝒇(and(( 𝒇 ∘ 𝒈 𝒙 .( 25.(( 𝒉 𝒙 = ( ( ( ( ( ( ( ( (

𝟑

27.((

𝟑 ( 𝟐𝒙 + 𝟒

( ( ( ( ( ( (

𝒉 𝒙 =

𝒙𝟑 − 𝟐𝟑(

26.( 𝒉 𝒙 = 𝟒𝒙 − 𝟐𝟏 ( &

( (

28.( 𝒉 𝒙 = 𝒙𝟐 − 𝟑𝒙 𝟔 ( ( &

( (

Copyright © PreCalculusCoach.com

& & & & & & & & &

4

( ( ( ( ( ( ( ( ( ( (

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& ANSWERS( Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 + 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 1.( (

3.(

(

𝒇 𝒙 = 𝟕𝒙 + 𝟏)( 𝒈 𝒙 = 𝟐𝒙 − 𝟗( 𝒇 + 𝒈 𝒙 = (𝟕𝒙 + 𝟏)) + (𝟐𝒙 − 𝟗 )( 𝒇 + 𝒈 𝒙 = 𝟗𝒙 − 𝟖( 𝑫𝒇9𝒈 = (−∞, ∞)( ( 𝒇 𝒙 = 𝒙 + 𝟏)( 𝒈 𝒙 = 𝒙 − 𝟒(

2.(

𝒇 + 𝒈 𝒙 = ( 𝒙 + 𝟏))) + ( 𝒙 − 𝟒)( 𝑫𝒇9𝒈 = 𝑫𝒇 ∩ 𝑫𝒈 ( 𝑫𝒇 = −𝟏, ∞ ( 𝑫𝒈 = 𝟒, ∞ ( 𝑫𝒇9𝒈 = −𝟏, ∞ ∩ 𝟒, ∞ ( 𝑫𝒇9𝒈 = 𝟒, ∞ ( (

(

(

4.(

𝒇 𝒙 = 𝟐𝒙𝟑 + 𝟏)( 𝒈 𝒙 = 𝟐𝒙𝟐 − 𝟏( 𝒇 + 𝒈 𝒙 = (𝟐𝒙 𝟑 + 𝟏))) + (𝟐𝒙𝟐 − 𝟏)( 𝒇 + 𝒈 𝒙 = 𝟐𝒙𝟑 + 𝟐𝒙𝟐 ( 𝑫𝒇9𝒈 = (−∞, ∞)& 𝟕𝒙) ( 𝟐 𝒙) 𝒈 𝒙 = ( 𝟔 𝒇 𝒙 =

𝟕𝒙) 𝒙) ( + 𝟔 𝟐 𝟐𝟐𝒙) 𝟏𝟏𝒙) = ( 𝒇+𝒈 𝒙 = 𝟑 𝟔 𝑫𝒇9𝒈 = (−∞, ∞)( 𝒇+𝒈 𝒙 =

( Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 − 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 5.( (

7.(

(

𝒇 𝒙 = 𝟓𝒙( 𝒈 𝒙 = 𝟐𝒙 − 𝟏𝟎( 𝒇 − 𝒈 𝒙 = 𝟓𝒙) − (𝟐𝒙 − 𝟏𝟎)( 𝒇 − 𝒈 𝒙 = 𝟑𝒙 + 𝟏𝟎( ( 𝑫𝒇=𝒈 = (−∞, ∞)( ( 𝟏 𝒇 𝒙 =𝟒− ( 𝒙 𝟏 𝒈 𝒙 =𝟕+ ( 𝒙 𝟏 𝟏 𝒇−𝒈 𝒙 = 𝟒− ) − 𝟕+ ( 𝒙 𝒙 𝟏 𝟏 𝒇−𝒈 𝒙 = 𝟒− −𝟕− ( 𝒙 𝒙 𝟐 𝒇 − 𝒈 𝒙 = −𝟑 − ( 𝒙 ( 𝑫𝒇=𝒈 = 𝑫𝒇 ∩ 𝑫𝒈 ( 𝑫𝒇 = (−∞, 𝟎) ∪ (𝟎, ∞)( 𝑫𝒈 = (−∞, 𝟎) ∪ (𝟎, ∞)( 𝑫𝒇=𝒈 = (−∞, 𝟎) ∪ (𝟎, ∞)( (

6.( (

8.(

(

𝒙) ( 𝟐 𝒈 𝒙 = 𝒙 − 𝟑( 𝒇 𝒙 =

𝒙) − 𝒙−𝟑 ( 𝟐 𝒙−𝟐 𝒙−𝟑 𝒇−𝒈 𝒙 = ( 𝟐 𝒇−𝒈 𝒙 =

( ( 𝑫𝒇=𝒈 = 𝑫𝒇 ∩ 𝑫𝒈 ( 𝑫𝒇 = (−∞, ∞)( 𝑫𝒈 = [𝟑, ∞)( 𝑫𝒇=𝒈 = [𝟑, ∞)( (

( ( Copyright © PreCalculusCoach.com

𝒇 𝒙 = 𝒙𝟐 + 𝟑𝒙 − 𝟐)( 𝒈 𝒙 = 𝟑𝒙𝟐 + 𝟐𝒙 − 𝟏( 𝒇 − 𝒈 𝒙 = 𝒙𝟐 + 𝟑𝒙 − 𝟐))) − (𝟑𝒙 𝟐 + 𝟐𝒙 − 𝟏)( 𝒇 − 𝒈 𝒙 = −𝟐𝒙 𝟐 + 𝒙 − 𝟏( ( 𝑫𝒇=𝒈 = (−∞, ∞)&

5

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& ( Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 𝒇 ∗ 𝒈 𝒙 .(Determine(the(domain(of(each(new(function.( 9.( (

10.( 𝒇 𝒙 = 𝟓𝒙𝟐 + 𝟐𝒙)( 𝒈 𝒙 = 𝒙𝟑 − 𝟒𝒙 − 𝟏( ( 𝒇 ∗ 𝒈 𝒙 = 𝟓𝒙𝟐 + 𝟐𝒙)) ∗ (𝒙𝟑 − 𝟒𝒙 − 𝟏)( 𝒇 ∗ 𝒈 𝒙 = 𝟓𝒙𝟓 + 𝟐𝒙𝟒 − 𝟐𝟎𝒙𝟑 − 𝟏𝟑𝒙𝟐 − 𝟐𝒙( ( ( 𝑫𝒇∗𝒈 = (−∞, ∞)( & 𝒙 + 𝟐) 12.( 𝒇 𝒙 = ( 𝟐 𝒙 − 𝟏) 𝒈 𝒙 = ( 𝟑 𝒙 + 𝟐) 𝒙 − 𝟏) ( ( 𝒇∗𝒈 𝒙 = ∗ 𝟑 𝟐 𝒙𝟐 − 𝒙 + 𝟐𝒙 − 𝟐) 𝒇∗𝒈 𝒙 = ( 𝟔 𝟐 𝒙 + 𝒙 − 𝟐)) ( 𝒇∗𝒈 𝒙 = 𝟔 ( ( 𝑫𝒇∗𝒈 = (−∞, ∞)(

𝒇 𝒙 = 𝟔𝒙)( 𝒈 𝒙 = 𝟒𝒙 − 𝟏( 𝒇 ∗ 𝒈 𝒙 = (𝟔𝒙) ∗ (𝟒𝒙 − 𝟏))( 𝒇 ∗ 𝒈 𝒙 = 𝟐𝟒𝒙𝟐 − 𝟔𝒙( ( ( 𝑫𝒇∗𝒈 = (−∞, ∞)( (

11.(

𝒇 𝒙 = 𝒙 + 𝟏)( 𝒈 𝒙 = 𝟐 𝒙 − 𝟏(

(

𝒇 ∗ 𝒈 𝒙 = 𝒙 + 𝟏) ∗ 𝟐 𝒙 − 𝟏 ( ) 𝒇 ∗ 𝒈 𝒙 = 𝟐 (𝒙 + 𝟏)(𝒙 − 𝟏)( 𝒇 ∗ 𝒈 𝒙 = 𝟐 𝒙𝟐 − 𝟏( ( 𝑫𝒇∗𝒈 = 𝑫𝒇 ∩ 𝑫𝒈 ( 𝑫𝒇 = −𝟏, ∞ ( 𝑫𝒈 = 𝟏, ∞ ( 𝑫𝒇∗𝒈 = −𝟏, ∞ ∩ 𝟏, ∞ ( 𝑫𝒇∗𝒈 = 𝟏, ∞ ( (

Using(𝒇 𝒙 (and(𝒈 𝒙 (find( 13.( (

𝒇 𝒈

𝒙 .(Determine(the(domain(of(each(new(function.( 14.( 𝒇 𝒙 = 𝟐𝒙𝟐 + 𝒙 − 𝟑 ( 𝒈 𝒙 = 𝒙 − 𝟑( ( 𝒇 𝟐𝒙𝟐 + 𝒙 − 𝟑 𝒙 = ( 𝒙−𝟑 𝒈 ( 𝑫 𝒇 = (−∞, 𝟑) ∪ (𝟑, ∞)(

𝒇 𝒙 = 𝟒𝒙 − 𝟏)( 𝒈 𝒙 = 𝒙 − 𝟒( 𝒇 𝟒𝒙 − 𝟏 𝒙 = ( 𝒙−𝟒 𝒈 ( 𝑫 𝒇 = (−∞, 𝟒) ∪ (𝟒, ∞)( 𝒈

𝒈

& 15.(

(

𝒇 𝒙 = 𝒙𝟐 − 𝟑𝟔( 𝒈 𝒙 = 𝒙 − 𝟔(

𝒇 𝒈 𝒇

𝒙 =

16.(

𝒙𝟐 − 𝟑𝟔 (𝒙 + 𝟔)(𝒙 − 𝟔) = ( 𝒙−𝟔 𝒙−𝟔

(

𝒙 = 𝒙 + 𝟔( 𝒈 𝑫 𝒇 = (−∞, 𝟔) ∪ (𝟔, ∞)( 𝒈

𝒙 + 𝟏) ( 𝟐 𝒙 − 𝟏) 𝒈 𝒙 = ( 𝟑 𝒙 + 𝟏) 𝒇 𝒙 = 𝟐 =( 𝒙 − 𝟏) 𝒈 𝟑 𝒇 𝟑(𝒙 + 𝟏)) 𝒙 = ( 𝟐(𝒙 − 𝟏) 𝒈 𝑫 𝒇 = (−∞, 𝟏) ∪ (𝟏, ∞)( 𝒇 𝒙 =

𝒈

(

Copyright © PreCalculusCoach.com

6

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& Find(each(composite(function.(Determine(the(domain(of(each(composite(function.( 17.(( 𝒇 𝒙 = 𝒙 + 𝟐)((((((((((𝒈 𝒙 = 𝒙 − 𝟒( 𝒇 ∘ 𝒈 𝒙 =?(((((((((((((𝑫𝒇∘𝒈 =?(

18.(

(

(&

19.((

𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝒇 𝒈 𝒙 = 𝒈 𝒙 + 𝟐( 𝒇 𝒈 𝒙 = 𝒙 − 𝟒 + 𝟐( 𝒇 𝒈 𝒙 = 𝒙 − 𝟐( &&&&) 𝑫𝒇∘𝒈 = (−∞, ∞)&&&&(

𝟏 𝟒 )))))))𝒈 𝒙 = ( 𝒙 𝒙+𝟏 𝒇 ∘ 𝒈 𝒙 =?((((𝑫𝒇∘𝒈 =?(

𝒇 𝒙 =

𝒈∘𝒇 𝒙 = 𝒈 𝒇 𝒙 ( 𝒈 𝒇 𝒙

20.(

(

(& 𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝟏 𝟒 𝒇 𝒈 𝒙 = )))))))))) ≠ 𝟎))))))))𝒙 ≠ 𝟎)))))))( 𝒙 𝒈 𝒙 +𝟏 𝟒 𝟏 )))))))))))))))) + 𝟏 ≠ 𝟎))))))𝒙 ≠ −𝟒( 𝒇 𝒈 𝒙 = 𝟒 𝒙 +𝟏 𝒙 𝒙 𝒇 𝒈 𝒙 = & 𝟒+𝒙 &&&) 𝑫𝒈 = (−∞, 𝟎) ∪ (𝟎, ∞)( 𝑫𝒇∘𝒈 = (−∞, −𝟒) ∪ (−𝟒, 𝟎) ∪ (𝟎, ∞)& &&&&& Find(and(then(evaluate(each(composite(function.(

21.(( 𝒇 𝒙 = 𝟕 − 𝒙))))))𝒈 𝒙 = 𝒙𝟐 − 𝟐𝒙 − 𝟐( 𝒇 ∘ 𝒈 𝟏 =?(

22.(

(

(&

𝟐

+ 𝟑(

𝒈 𝒇 𝒙 = 𝒙 − 𝟏 + 𝟑))))))𝒙 − 𝟏 ≥ 𝟎)))))𝒙 ≥ 𝟏)))))( 𝒈 𝒇 𝒙 = 𝒙 − 𝟏 + 𝟑( 𝒈 𝒇 𝒙 = 𝒙 + 𝟐( ( 𝑫𝒇 = [𝟏, ∞)( 𝑫𝒈∘𝒇 = [𝟏, ∞)( 𝒙𝟐 )))))))𝒈 𝒙 = 𝒙 − 𝟔( 𝒇 𝒙 = 𝟑 𝒈 ∘ 𝒇 𝒙 =?((((𝑫𝒈∘𝒇 =?( ( 𝒈∘𝒇 𝒙 = 𝒈 𝒇 𝒙 ( 𝒈 𝒇 𝒙 = 𝒇 𝒙 − 𝟔)))))))))))))))))))))))))( 𝒙𝟐 − 𝟔))))))))))))))))))( 𝒈 𝒇 𝒙 = 𝟑 𝟐 𝒙 − 𝟏𝟖 & 𝒈 𝒇 𝒙 = 𝟑 &&&) 𝑫𝒇 = (−∞, ∞)( 𝑫𝒈∘𝒇 = (−∞, ∞)& (

𝒇 𝒙 = 𝒈∘𝒇 𝒈∘𝒇 𝒈 𝒇 𝒙 𝒈 𝒇 𝒙 𝒈 𝒇 𝒙 ( 𝒈 𝒇 𝟑 𝒈 𝒇 𝟑

(((( ( Copyright © PreCalculusCoach.com

= 𝒇 𝒙

𝟐

(

𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝒇 𝒈 𝒙 = 𝟕 − 𝒈 𝒙 ))))))( 𝒇 𝒈 𝒙 = 𝟕 − (𝒙𝟐 − 𝟐𝒙 − 𝟐)))))))( 𝒇 𝒈 𝒙 = −𝒙𝟐 + 𝟐𝒙 + 𝟗( ( 𝒇 𝒈 𝟏 = −𝟏𝟐 + 𝟐 ∗ 𝟏 + 𝟗( 𝒇 𝒈 𝟏 = 𝟏𝟎( &&&&&&&&&&(

𝒇 𝒙 = 𝒙 − 𝟏)((((((((((𝒈 𝒙 = 𝒙 𝟐 + 𝟑( 𝒈 ∘ 𝒇 𝒙 =?(((((((((((𝑫𝒈∘𝒇 =?(

7

𝟑) 𝒙 ))))))))𝒈 𝒙 = ( 𝟐 𝒙 𝟑 =?( 𝒙 =𝒈 𝒇 𝒙 ( 𝒇 𝒙 = ( 𝟐 𝟑) = 𝒙 )( 𝟐 𝟑 = ( 𝟐𝒙 𝟑 ) 𝟐∗𝟑 𝟏 = ( 𝟐

=

Name:&_________________________________________________&Period:&___________&Date:&________________&

Function(Operations(and(Composition(of(Functions(Assignment& 23.(( 𝒇 𝒙 = 𝟏 − 𝟐𝒙))))))𝒈 𝒙 = 𝒙 + 𝟏( 𝒇 ∘ 𝒈 −𝟏 =?(

24.(

(

(&

𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝒇 𝒈 𝒙 = 𝟏 − 𝟐 ∗ 𝒈 𝒙 ))))))( 𝒇 𝒈 𝒙 = 𝟏 − 𝟐 ∗ 𝒙 + 𝟏))))))))))))( 𝒇 𝒈 𝒙 = 𝟏 − 𝟐 𝒙 + 𝟏( ( 𝒇 𝒈 −𝟏 = 𝟏 − 𝟐 −𝟏 + 𝟏( 𝒇 𝒈 −𝟏 = 𝟏( &&&&&&&&&&(

𝒇 𝒙 = 𝒈∘𝒇 𝒈∘𝒇 𝒈 𝒇 𝒙 𝒈 𝒇 𝒙 𝒈 𝒇 𝒙

𝒙 − 𝟒) 𝟐𝒙 ))))))))𝒈 𝒙 = ( 𝟑 𝟐 −𝟐 =?( 𝒙 =𝒈 𝒇 𝒙 ( 𝟐∗𝒇 𝒙 ( = 𝟑 𝒙 − 𝟒) 𝟐∗ 𝟐 = ( 𝟑 𝒙−𝟒 ( = 𝟑

( 𝒈 𝒇 −𝟐

𝒈 𝒇 −𝟐 (((( Express)𝒉 𝒙 (as(a(composition(of(two(functions(𝒇(and(( 𝒇 ∘ 𝒈 𝒙 .( 25.(( 𝒉 ( ( 𝒉 ( 𝒉 ( 𝒇 ( ( ( 𝒇 ( 𝒈 ( 27.((

𝒙 =

𝟑

26.( 𝒉 𝒙 = 𝟒𝒙 − 𝟐𝟏 (

𝒙𝟑 − 𝟐𝟑(

𝟑

𝒙 = 𝒙𝟑 − 𝟐𝟑( 𝒙 = 𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝒈 𝒙

=

𝟑

𝒈 𝒙 =

𝟑

𝒙𝟑 − 𝟐𝟑 (

𝟑 ( 𝟐𝒙 + 𝟒 𝒉 𝒙 = 𝒇∘𝒈 𝒙 = 𝒇 𝒈 𝒙 ( 𝟑 𝟑 𝒇 𝒈 𝒙 = = ( 𝒈 𝒙 + 𝟒 𝟐𝒙 + 𝟒 ( 𝒉 𝒙 =

𝒇 𝒙 =

𝟑 (((((((((((((𝒈 𝒙9𝟒

𝒉 𝒉 𝒇 & 𝒇 𝒈

𝒙 = 𝟒𝒙 − 𝟐𝟏 ( 𝒙 = 𝒇∘𝒈 𝒙 =𝒇 𝒈 𝒙 ( 𝒈 𝒙 = 𝒈 𝒙 = 𝟒𝒙 − 𝟐𝟏 & 𝒙 = 𝒙( 𝒙 = 𝟒𝒙 − 𝟐𝟏&

28.( 𝒉 𝒙 = 𝒙𝟐 − 𝟑𝒙 𝟔 ( (

𝟑 ( 𝟐𝒙 + 𝟒

( ( ( ( ( ( ( (

&

𝒙 = 𝟑 𝒙( 𝒙 = 𝒙𝟑 − 𝟐𝟑(

𝒉 𝒙 =

−𝟐 − 𝟒 −𝟔 ) = 𝟑 𝟑 = −𝟐( =

&

𝟔

𝟔

𝒇 𝒈 𝒙 = 𝒈 𝒙 = 𝒙𝟐 − 𝟑𝒙 & & ( 𝒇 𝒙 = 𝒙𝟔 (((((((((((𝒈 𝒙 = 𝒙𝟐 − 𝟑𝒙(

𝒙 = 𝟐𝒙(

( (

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𝟔

𝒉 𝒙 = 𝒙𝟐 − 𝟑𝒙 ( 𝒉 𝒙 = 𝒇∘𝒈 𝒙 =𝒇 𝒈 𝒙 (

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