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the amount a plumber charges can be modeled by the function f(x) = 75 + 49x where x is the number of hours worked. (a) Find an equation for the inverse of the function.(b) if the electrician charges $225 how many hours did the job last?



Answer :

The inverse of a function f(x) is obtained by asuuming f(x)=y, and then solving for x, and then replacing x by y .

Given data:

it is given that the amount a plumber charges is modeled by f(x) = 75 +49x

(a)

Now to find the inverse of the function let f(x)=y so that

[tex]\begin{gathered} 75+49x=y \\ 49x=y-75 \\ x=\frac{y-75}{49} \end{gathered}[/tex]

Now on replacing y by x we get:

[tex]f^{-1}(x)=\frac{x-75}{49}[/tex]

which is the inverse of the function.

(b) Now if he charges $225 then we have,

[tex]\begin{gathered} 225=75+49x \\ 49x=225-75 \\ 49x=150 \\ x=\frac{150}{49} \\ x=3.06 \end{gathered}[/tex]

so, the jobs last for 3.06 hours.

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