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45

Step-by-step Answer
PAGE: 71SET: ExercisesPROBLEM: 45
Please look in your text book for this problem Statement

Average exchange rate from Euros to US dollars is .

(a)

Horizontal line test:

A function has an inverse if and only if no horizontal line intersects its graph of the function in at most one point.

Graph :

Graph  the function .

Draw the horizontal line .

Observe the graph:

The horizontal line touches the graph of the function at only one point.

The function is an one-to-one, because it  passes the horizontal line test.

Therefore the inverse of the function exist.

To find the inverse of the function, consider and solve in terms of .

Now interchange and .

Replace .

The inverse of is .

(b).

The inverse of the function is .

Here represents the value of  currency in  US dollars and represents the currency value in Euros.

Hence represents the average exchange rate from US dollars to Euros.

(c).

In the function , represents the average exchange rate from Euros to US.

The exchange rate should be positive i.e. .

(d)

Find the value of 100 US dollars in Euro.

Average exchange rate from US dollars to Euros is .

Substitute in .

.

Therefore  US dollars equals to  Euros.

(a)The inverse of is .

(b) represents the average exchange rate from US dollars to Euros.

(c) The exchange rate should be positive i.e. .

(d) US dollars equals to  Euros.



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