Questions from General Calculus

Q: (a). If and g (x) = 2x +

(a). If and g (x) = 2x + 1, find h (x) = 4x2 + 4x + 7 find a function f such that f 0 g. (Think about what operations you would have to perform on the formula for to end up with the formula for g.) (b...

Q: The functions in Example 10 and Exercise 61(a) are

The functions in Example 10 and Exercise 61(a) are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life. Exercise 61(a):...

Q: In a certain country, income tax is assessed as follows.

In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000...

Q: Suppose t is an odd function and let h = f 0

Suppose t is an odd function and let h = f 0 g. Is h always an odd function? What if f is odd? What if f is even?

Q: (a). If the point (5, 3) is

(a). If the point (5, 3) is on the graph of an even function, what other point must also be on the graph? (b). If the point (5, 3) is on the graph of an odd function, what other point must also be on...

Q: A function f has domain [-5, 5] and a

A function f has domain [-5, 5] and a portion of its graph is shown. (a). Complete the graph of f if it is known that f is even. (b). Complete the graph of f if it is known that f is odd.

Q: Graphs of f and g are shown. Decide whether each function

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.

Q: In this section we discussed examples of ordinary, everyday functions:

In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time. Give three other...

Q: Find the functions (a) f0g, (b) g0f

Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains.

Q: The graphs of f and t are given. /

The graphs of f and t are given. (a). State the values of f (-4) and g (3). (b). For what values of is f (x) – g (x)? (c). Estimate the solution of the equation f (x) = -1. (d). On...