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Chapter 1: Problem 3

Evaluate the indicated expression assuming that \(f, g,\) and \(h\) are the functions completely defined by these tables: $$\begin{array}{c|c}x & f(x) \\\\\hline 1 & 4 \\\2 & 1 \\\3 & 2 \\\4 & 2\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 1 & 2 \\\2 & 4 \\\3 & 1 \\\4 & 3\end{array}$$ $$\begin{array}{c|c}x & h(x) \\\\\hline 1 & 3 \\\2 & 3 \\\3 & 4 \\\4 & 1\end{array}$$ \((g \circ f)(1)\)

Short Answer

Expert verified
Therefore, the short answer is: \((g \circ f)(1) = 3\).

Step by step solution

01

Find f(1)

From the table of f(x), we can see that f(1) = 4.
02

Evaluate g at the result of f(1)

Now, we need to evaluate g at x = 4 (since f(1) = 4). From the table of g(x), we can see that g(4) = 3.
03

Write the resulting value of (g 鈿� f)(1)

Since g(4) = 3, the expression (g 鈿� f)(1) is equal to 3.

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Most popular questions from this chapter

A temperature \(F\) degrees Fahrenheit corresponds to \(g(F)\) degrees on the Kelvin temperature scale, where $$g(F)=\frac{5}{9} F+255.37$$ (a) Find a formula for \(g^{-1}(K)\). (b) What is the meaning of \(g^{-1}(K) ?\) (c) Evaluate \(g^{-1}(0)\). (This is absolute zero, the lowest possible temperature, because all molecular activity stops at 0 degrees Kelvin.)

Check your answer by evaluating the appropriate function at your answer. Suppose \(h(t)=\frac{2-3 t}{4+5 t}\), Find a formula for \(h^{-1}\).

Suppose you are exchanging cur. rency in the London airport. The currency exchange service there only makes transactions in which one of the two currencies is British pounds, but you want to exchange dollars for Euros. Thus you first need to exchange dollars for British pounds, then exchange British pounds for Euros. At the time you want to make the exchange, the function \(f\) for exchanging dollars for British pounds is given by the formula \(f(d)=0.66 d-1\) and the function \(g\) for exchanging British pounds for Euros is given by the formula \(g(p)=1.23 p-2\) The subtraction of 1 or 2 in the number of British pounds or Euros that you receive is the fee charged by the currency exchange service for each transaction. Which process gives you more Euros: exchanging $$\$ 100$$ for Euros twice or exchanging $$\$ 200$$ for Euros once?

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Show that the sum of two even functions (with the same domain) is an even function.
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