# The function that converts the dollars of Country A to the dollars of Country B

The function that converts the dollars of Country A to the dollars of Country B according to January 13, 2008, values is $f\left(x\right)=0.99286x$, where x is the number of dollars of Country A and f(x) is the number of dollars of Country B. Complete parts a and b below.
a. Find the inverse function for f.
${f}^{-1}\left(x\right)=$___
(Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

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Step 1
Given: $f\left(x\right)=0.99286x\to \left(1\right)$,
where x is the number of dollars of country A
let $y=f\left(x\right)\to \left(2\right)$ is the number of dollars of country B
therefore, $x={f}^{-1}\left(y\right)$
Step 2
substitute Eq'n(2) in Eq'n(1)
$y=0.99288x$
$x=\frac{y}{0.99288}$
${f}^{-1}\left(y\right)=1.00717y$
Substitute x insted of y therefore,
${f}^{-1}\left(x\right)=1.00717x$