Solution Found!
Explain why or why not Determine whether the
Chapter 6, Problem 55E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The range of f(x) = 2x - 38 is all real numbers.
b. The relation \(f(x)=x^{6}+1\) is not a function because f(1) = f(-1) = 2
c. If \(f(x)=x^{-1}\), then f(1/x) = 1/f(x).
d. In general, \(f(f(x))=(f(x))^{2}\).
e. In general, f(g(x)) = g(f(x)).
f. In general, \(f(g(x))=(f\ \circ\ g)(x)\)
g. If f(x) is an even function, then cf(ax) is an even function, where a and c are real numbers.
h. If f(x) is an odd function, then f(x) + d is an odd function, where d is a real number.
i. If f is both even and odd, then f(x) = 0 for all x.
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The range of f(x) = 2x - 38 is all real numbers.
b. The relation \(f(x)=x^{6}+1\) is not a function because f(1) = f(-1) = 2
c. If \(f(x)=x^{-1}\), then f(1/x) = 1/f(x).
d. In general, \(f(f(x))=(f(x))^{2}\).
e. In general, f(g(x)) = g(f(x)).
f. In general, \(f(g(x))=(f\ \circ\ g)(x)\)
g. If f(x) is an even function, then cf(ax) is an even function, where a and c are real numbers.
h. If f(x) is an odd function, then f(x) + d is an odd function, where d is a real number.
i. If f is both even and odd, then f(x) = 0 for all x.
ANSWER:Step-by-step solution Step 1 of 9 (a) Different functions have defined domain by its definition. In this case f is polynomial function and the range of all polynomial functions is all reals numbers . Therefore, the answer is true.