Name______Date______
Algebra 2 / Trig
Worksheet – Inverse Functions
1. To determine whether a relation is a function, we use the vertical line test (VLT). To determine whether the inverse of a relation is a function, we use the horizontal line test (HLT). The HLT says that if you can draw a horizontal line anywhere on the graph of a relation, then the inverse of the relation is a function.
Using this important knowledge, sketch graphs of the functions below, then use the HLT to determine if the inverse of the function is also a function.
If the inverse is not a function, restrict the domain of the function so that the inverse is a function.
a) f(x) = |x| b) f(x) = x3
c) f(x) = sin x d) f(x) = x3 + 2x2 – 3x – 4
2. Decide whether the function with the given equation is even, odd, or neither. Justify your answer algebraically.
Remember: even function à f(–x) = f(x) odd function à f(–x) = –f(x)
a. s(t) = 8t7 b. f(x) = 7x5 – 5x2 c. g(h) = -9h2 + 5 d. v(m) = |7m + 2| – 5
3. Decide whether the function is even, odd, or neither.
a. b.
4. Describe the symmetries of the graphed function.
a. b.
5. Let f(x) = x2 + 2x + 7 and g(x) = 5x – 3.
a. Evaluate f(g(1)) b. Evaluate g(f(1))
c. Find f(g(x)) d. Find g(g(x))
6. Let and n(x) = x2 – 2. Give the domain of each composite.
a. b.
7. For each function described below:
a. Give an equation for the inverse of the function.
b. State whether the inverse is a function.
y = 3 – 2x a.______b.______
a.______b.______
f = {(-2, 0), (0, -3), (1, 3), (-3, 1)}
a.______b.______
8. True or false. If a function is an even function, then its inverse is not a function.
Justify your answer.
9. Show algebraically that f(x) = x3 + 1 and are inverses by showing that f(g(x)) = x and g(f(x)) = x.
10. Determine whether the inverse of the graphed function is a function. If the inverse is a function, sketch its graph on the same set of axes.
a. b. c.
11. Let .
True or false. The domain of p is the same as the domain of .
Justify your answer.