# College Algebra Problems With Answers sample 2 : Composite and Inverse Functions

College algebra problems and questions on composite and inverse functions are presented along with their solutions located at the bottom of the page.

1. Let f(x) = √(x - 4) + 3.
a) Find the inverse of f.
b) Find the range of f -1.
2. Let h(x) = (x - 1) / (-x + 3).
a) Find the inverse of h.
b) Find the range of h.
3. Let f(x) = (x - 1)/(x + 5) and g(x) = 1/(x + 3).
a) Find the composite function (f o g)(x).
b) Find the domain of f o g.
4. Function f is a function with inverse f -1. Function h is defined by h(x) = f(x) + k where k is a constant. Express the inverse function of h in terms of f -1 and k.
5. Function f is a function with inverse f -1. Function h is defined by h(x) = A*f(x - h) + k where A, k and h are constants. Express the inverse function of h in terms of f -1, A, k and h.
6. The graphs of functions f and g are shown below.
a) Use the graph to find (f o g)(-4)
b) Use the graph to find (g o f)(1) Figure 1. Graph of Function f Figure 2. Graph of Function g
7. Functions f and h are defined by the tables
 x -3 -2 -1 0 1 2 3 f(x) -6 -4 -2 1 2 6 16

 x 0 1 2 3 4 5 6 h(x) 1 2 5 10 17 26 37

Use the values in the tables to find
a) (f o h)(1)
b) (f o f)(0)
c) (f o h)(5)
d) (f o h-1)(5)
e) (h o f-1)(6)

1. f -1(x) = (x - 3)3 + 4 , x≥3
2. [4 , +infinity) : it is the domain of f

1. h -1(x) = (-3x - 1) / (x + 1)
2. (-infinity , -1) U (-1 , +infinity) : it is the domain of h-1

1. (f o g)(x) = -(x + 2) / (5x + 16)
2. domain of the composite function f o g : (-infinity , -16/5) U (-16/5 , -3) U (-3 , +infinity)

1. h -1(x) = f -1(x - k)
2. h -1(x) = f -1((x - k) / A) + h
1. (f o g)(-4) = f(g(-4)) = f(2) = -2
2. (g o f)(1) = g(f(1) = g(-3) = -1

1. (f o h)(1) = f(h(1)) = f(2) = 6
2. (f o f)(0) = f(f(0)) = f(1) = 2
3. (f o h)(5) = f(h(5) = f(26) = undefined
4. (f o h-1)(5) = f(h-1(5)) = f(2) = 6
5. (h o f-1)(6) = h(f-1(6)) = h(2) = 5