Download Solving Functional Equations & Graphing Functions: Composites, Inverses, & Logarithms and more Exercises Algebra in PDF only on Docsity!
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Composites, Inverse Functions, and Logarithms
- Let f ( x ) x 5 and ( ) 7
2 g x x
a. Find ( f g )( x ).
b. Find ( f g )( 2 ).
c. Find (^) ( g f )( x ).
d. Find (^) ( g f )( 2 ).
- Let f ( x ) 3 x 6. Find the inverse function, ( )
1 f x , and verify that(^ f^ f )( x ) x
1 and
( f f )( x ) x
1 . Then, graph both functions on the same axis.
x y 3 x 6 y ( x , y ) ( y , x )
- Let ( ) 4
3 f x x. Find the inverse function, ( )
1 f x , and verify that( f f )( x ) x
1 and
( f f )( x ) x
1 . Then, graph both functions on the same axis.
x 4
3
y x y (^ x , y ) (^ y , x )
x
y
x
y
- Graph
x f^ (^ x )^2 and x
g x 2
( ) on the same axis.
x y 2 x y ( x , y )
- Graph f ( x ) log 2 x and g x x
2
( ) log 1 on the same axis.
x y y (^ x , y ) (^ y , x )
x y y (^ x , y ) (^ y , x )
x x
y 2
y ( x , y )
x
y
x
y
Answers:
- a.( )() 2
2 f g x x
b.( f g )( 2 ) 2
c.( g f )( x ) x 2
d.( g f )( 2 ) 0
- x^ log ay
64 y
y
- log 3 log ( 2 ) 5 log( 1 ) 2
9 x 9 x 9 x
7
3
12
log x
x
log x
x
x g x x f ( x ) 2 2
(^1 ) ( ) 4 f ( x ) x 4
3 f x x
1 x f ( x ) 3 x 6 f x
f ( x ) log 2 x
gx x
2
( ) log 1
