Questions from General Calculus

Q: Let g(x) = 3 1 − x3

Let g(x) = 3 1 − x3 . a. Find g-1. How is it related to g? b. Graph g. How do you explain your answer to part (a)?

Q: a. How is the logarithmic function y = logbx defined?

a. How is the logarithmic function y = logbx defined? b. What is the domain of this function? c. What is the range of this function? d. Sketch the general shape of the graph of the function y = log...

Q: a. What is the natural logarithm? b. What

a. What is the natural logarithm? b. What is the common logarithm? c. Sketch the graphs of the natural logarithm function and the natural exponential function with a common set of axes.

Q: Find the exact value of each expression. a. log232

Find the exact value of each expression. a. log232 b. log82

Q: Find the exact value of each expression. a. log5

Find the exact value of each expression. a. log5 1/125 b. ln(1/e2)

Q: Find the exact value of each expression. a. log1040

Find the exact value of each expression. a. log1040 + log102.5 b. log860 - log83 - log85

Q: If f(x) = 3x2 - x + 2,

If f(x) = 3x2 - x + 2, find f(2), f(-2), f(a), f(-a), f(a + 1), 2f(a), f(2a), f(a2), [ f(a)]2, and f(a + h).

Q: Find the exact value of each expression. a. e

Find the exact value of each expression. a. e-ln2 b. e ln(ln e 3)

Q: Express the given quantity as a single logarithm. ln 10

Express the given quantity as a single logarithm. ln 10 + 2 ln 5

Q: Express the given quantity as a single logarithm. ln b

Express the given quantity as a single logarithm. ln b + 2 ln c – 3 ln d