# Composition of Functions

1. If
and k(x) = 3x − 5, find each of the following.

(a) f(g(x))

(b) g(f(x))

(c) f(g(k(x)))

(d) k(k(x))

2. How many ways can you find to decompose the function

into functions f and g such that f(g(x)) = h(x)? For each possibility, list f and g.

3. Currency traders often move investments from one
country to another in order to make

a profit. The following table gives exchange rates for US dollars, Japanese yen,
and the

European Union’s euro on April 23, 2001.

Amount invested |
Dollars purchased |
Yen purchased |
European euro purchased |

1 dollar | 1.0000 | 121.17 | 1.1157 |

1 yen | 0.0083 | 1.0000 | 0.0092 |

1 euro | 0.8963 | 108.61 | 1.0000 |

For example, one US dollar purchases 121.17 Japanese yen
or 1.1157 European euros. Similarly,

one European euro purchases 108.61 Japanese yen or 0.8963 US dollars. Suppose

f(x) = Number of yen one can buy with x dollars

g(x) = Number of euros one can buy with x dollars

h(x) = Number of euros one can buy with x yen

(a) Find formulas for f , g, and h.

(b) Evaluate h(f(1000)) and interpret this in terms of currency .

4. A function f has an inverse if there exists a function
g such that

f(g(x)) = g(f(x)) = x.

We usually write f^{ −1} instead of g.

Important! f^{ −1} does not mean 1/f(x). |

Let f be given by the following table.

Complete the following table.

Can you find algebraic formulas related to f and f^{ −1}?

Prev | Next |