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Sagot :
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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