Chapter 1.5, Problem 33E

Solution

a.

To convert : The Euros for US dollar $\$100$ ,the exchange rate for converting US dollar $x$ to the euro $y$ is $y=0.76x$

The converting value of US dollar $\$100$ is $76\text{Euros}\text{.}$

Given information:

The given exchange rate for converting US dollar $x$ to the euro $y$ is $y=0.76x$ and the given us dollar is $\$100$ .

Concept used:

By substitution method can find the values of $y$ . .

Calculations:

Substitute each value of $x=100$ into the equation of $y$:

  $\begin{array}{c}y=0.76x\\ x=100\\ y=0.76\times 100\\ =76\end{array}$

Thus the converting value of US dollar $\$100$ is $76\text{Euros}\text{.}$

b.

To find : The inverse of the function $y=0.76x$ and describe its use.

The inverse of the given function is $f^{-1}(x)=\frac{x}{\mathrm{0.76.}}$ in this case the inverse function using for converting euro to US dollar.

Given information:

The given function $y=0.76x$

Concept used :

Algebraically can find out the inverse, first replace $x\text{a}sy\text{and}y\text{as}x$ and then solve for $y$ .

Calculations:

Here

  $\begin{array}{c}y=0.76x\\ \text{replace}x\text{and}\text{}y\\ x=0.76y\\ \text{Solve}\text{for}y\\ y=\frac{x}{0.76}\\ f^{-1}\left(x\right)=\frac{x}{0.76}\end{array}$

Hence the inverse function is $f^{-1}(x)=\frac{x}{\mathrm{0.76.}}$ and in this case the inverse function using for converting euro to US dollar.

c.

To convert: the $43\text{euro}\text{into}\text{US}\text{dollar}.$ the function is $y=\frac{x}{0.76}.$

The converting value of euro $43$ to Us dollar is about $56.58$ .

Given information:

The given equation is $y=\frac{x}{0.76}.$ .

Concept used :

By substitution method can find the values of $y$

Calculations:

Substitute each value of $x=43$ into the equation of $y$:

  $\begin{array}{c}y=\frac{43}{0.76}\\ \simeq 56.58\end{array}$

Thus the converting value of euro $43$ to Us dollar is about $56.58$