
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
- a. A function could have the property that f(−x) = f(x), for all x.
- b. cos (a + b) = cos a + cos b, for all a and b in [0, 2π].
- c. If f is a linear function of the form f(x) = mx + b, then f(u + v) = f(u) + f(v), for all u and v.
- d. The function f(x) = 1 − x has the property that f(f(x)) = x.
- e. The set {x: |x + 3| > 4} can be drawn on the number line without lifting your pencil.
- f. log10(xy) = (log10 x)(log10 y)
- g. sin−1 (sin (2π)) = 0
a.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is true.
Explanation of Solution
Given:
A function could have a property that
Consider the function
Then,
Therefore, the statement is true.
b.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The identity
Calculation:
Take
Then,
And,
That is,
Therefore, the statement is false.
c.

Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
If
Calculation:
Take
That is,
The right hand side of equation
And, the left hand side of equation
Thus,
Therefore, the statement is false.
d.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is true.
Explanation of Solution
Given:
The function
Calculation:
Consider the function
Then,
Therefore, the statement is true.
e.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The set
Calculation:
The given set
Therefore, the set
Therefore, the statement is false.
f.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The equation,
Calculation:
Take,
Then,
and,
Then,
Therefore, the statement is false.
g.

Whether the given statement is true or not and give an explanation or a counter example.
Answer to Problem 1RE
The statement is true.
Explanation of Solution
Given:
The equation,
Consider
Then, compute the following.
Thus,
Therefore, the statement is true.
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Chapter 1 Solutions
Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
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