Operations On Functions With Inverses

Unit Three – Operations on Functions 2 Given: f ( x ) = 2 x + 3 ; g ( x ) = 8 − 3 x and h ( x ) = x − 2 x + 4

Find each of the following: 1) ( f − g ) ( x )

2) ( h + f ) ( 2 )

5) ( f + g ) ( w + 2 )

6) ( f oh ) ( x )

3) ( f gh ) ( x )

h 7)   ( x )  f  9) ( f + ( g gh ) ) ( −1)

( ) 13) ( f o f ) ( x ) 11) g ( h ( 9 ) ) −1

g 15)   ( 6 )  f 

4) ( g oh ) ( 4 )

8) ( g og ) ( −3) 10) ( h og ) ( −5 ) 12) ( g − h ) ( x ) 14) ( h o f ) ( x ) 16) ( g o( f gh ) ) ( −5 )

Find the inverse of each of the following: 2 17) f ( x ) = 6 − 9 x 18) f ( x ) = x − 7 2 19) f ( x ) = x + 3 3 Determine if f(x) and g(x) are inverses using their compositions: 3 1 f x = x − 3 + 2; g ( x) = 3 x −2 +3 21) ( ) ( ) 20) f ( x ) = 2 x + 6; g ( x) = x − 3 2