Solution Found!
Figure 2-6e shows the graph of if x is rational if x is irrational a. Find f(2), f(3)
Chapter 2, Problem 4(choose chapter or problem)
Figure 2-6e shows the graph of
\(f(x)=\left\{\begin{array}{ll} 2^{x}, & \text { if } x \text { is rational } \\ 8, & \text { if } x \text { is irrational } \end{array}\right.\)
a. Find f(2), f(3), f(0.5), and \(f(\sqrt{5})\).
b. Is f continuous at x = 3? Explain.
c. Where else is f continuous? Surprising?
d. Because f(0) = 1 and f(2) = 4, is the intermediate value theorem true for all values of y between 1 and 4? Explain.
Questions & Answers
QUESTION:
Figure 2-6e shows the graph of
\(f(x)=\left\{\begin{array}{ll} 2^{x}, & \text { if } x \text { is rational } \\ 8, & \text { if } x \text { is irrational } \end{array}\right.\)
a. Find f(2), f(3), f(0.5), and \(f(\sqrt{5})\).
b. Is f continuous at x = 3? Explain.
c. Where else is f continuous? Surprising?
d. Because f(0) = 1 and f(2) = 4, is the intermediate value theorem true for all values of y between 1 and 4? Explain.
Step 1 of 5
The given function is
\(f(x)=\left\{\begin{array}{ll}
2^{x}, & x \text { is rational } \\
8, & x \text { is irrational }
\end{array}\right.\)