4. a. ( f o g o h )(x) = f o g[ h(x) ]

= f o g(x²)

= f[ 2(x²) - 1 ]

= f( 2x² - 1 )

= ( 2x² - 1 ) + 3

= 2x² + 2

( f o g o h )(0) = 2.0² + 4

= 4

b. ( g o f o h )(x) = g o f[ h(x) ]

= g o f(x²)

= g[ (x²) + 3 ]

= g( x² + 3 )

= 2( x² + 3 ) - 1

= 2x² + 6 - 1

= 2x² + 5

( g o f o h )(2) = 2.2² + 5

= 2.4 + 5

= 8 + 5 = 13

c. ( h o f o g )(x) = h o f[ g(x) ]

= h o f( 2x - 1 )

= h[ ( 2x - 1 ) + 3 ]

= h( 2x + 2 )

= ( 2x + 2 )²

= 4x² + 8x + 4

( h o f o g )(1) = 4.1² + 8.1 + 4

= 16

d. ( f o h o g )(x) = f o h[ g(x) ]

= f o h( 2x - 1 )

= f[ ( 2x - 1 )² ]

= f( 4x² - 4x + 1 )

= ( 4x² - 4x + 1 ) + 3

= 4x² - 4x + 4

( f o h o g )(½) = 4(½)² - 4.½ + 4

= 4.¼ - 2 + 4

= 1 + 2 = 3

e. ( g o h o f )(x) = g o h[ f(x) ]

= g o h( x + 3 )

= g[ ( x + 3 )² ]

= g( x² + 6x + 9 )

= 2( x² + 6x + 9 ) - 1

= 2x² + 12x + 18 - 1

= 2x² + 12x + 17

( g o h o f )(x) = 2(⅓)² + 12.⅓ + 17

= 2(1/9) + 4 + 17

= ( 2/9 ) + 21

= ( 2/9 ) + ( 189/9 )

= 191/9 = 21 2/9

5. a. f(x) = y

2x + 5 = y

2x = y - 5

b. g(x) = y

x - 2 = y

x = y + 2

g⁻¹(x) = x + 2

c. ( f o g )⁻¹(x) = g⁻¹ o f⁻¹

= g⁻¹[ f⁻¹ ]

d. ( g o f )⁻¹(x) = f⁻¹ o g⁻¹

= f⁻¹[ g⁻¹ ]

= f⁻¹( x + 2 )