Precalculus A
4.1-4.3 Review
Name __________________
1.
For the given functions f and g, find the requested composite function value.
f ( x)  2 x  4
g ( x)  2 x 2  5
(f
g )(3)
a)
(g
f )(2)
b)
2.
Find the indicated composite for the pair of functions.
1
7
f ( x) 
g ( x) 
x5
8x
(f
g )( x)
a)
(g
f )( x)
b)
c)
Are the functions inverses of one another? Explain why or why not.
3.
Find the functions f and g so that the composition of f and g is H ( x)  (5  2 x3 ) 2 .
4.
Graph
a)
b)
c)
d)
e)
5.
Verify that the functions are inverses of one another in two ways:
a) Algebraically (Find the composite functions f ( g ( x))  x and g ( f ( x))  x. )
b) Graphically (Are the graphs reflections over the line y  x ?)
x
f ( x)  4 x  8 and g ( x)   2
i.
4
ii.
f ( x)  x  1 ; x  1 and g ( x)  x 2 1; x  0
6.
Graph f ( x)  3 x  1 by hand. Begin by graphing f ( x)  3x and use transformations to graph the
function. State each transformation you used. State the domain, range and horizontal asymptote.
7.
The following functions are one-to-one. Find the inverse function.
7x  3
f ( x) 
f ( x)  5 x  8
a)
c)
3
3x  2
f ( x) 
f ( x)  3 x  8
b)
d)
x5
f ( x)  x 3 .
State the domain.
State the range.
Is the function one-to-one?
Graph the inverse function f 1 ( x) .
State its domain and range.
Solve
8.
5x 
1
25
9.
3 x 
1
81
11.
4(113 x )  16
12.
(e x ) x e18  e9 x
10.
31 2 x  243