Solution Found!
Explain why or why not. Determine whether the following
Chapter 5, Problem 1RE(choose chapter or problem)
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 \([0,\ 2\pi]\).
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. \(\log _{10}(x y)=\left(\log _{10} x\right)\left(\log _{10} y\right)\)
g. \(\sin ^{-1}(\sin (2 \pi))=0\)
Questions & Answers
QUESTION:
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 \([0,\ 2\pi]\).
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. \(\log _{10}(x y)=\left(\log _{10} x\right)\left(\log _{10} y\right)\)
g. \(\sin ^{-1}(\sin (2 \pi))=0\)
ANSWER:Step-by-step solution Step 1 a) We need to find whether the statement “A function could have the property that f(x) = f(x) for all x” is true or false.