Question

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 1

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

`\begin{gathered} 75+49x=y \\ 49x=y-75 \\ x=(y-75)/(49) \end{gathered}`

Now on replacing y by x we get:

`f^(-1)(x)=(x-75)/(49)`

which is the inverse of the function.

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

`\begin{gathered} 225=75+49x \\ 49x=225-75 \\ 49x=150 \\ x=(150)/(49) \\ x=3.06 \end{gathered}`

so, the jobs last for 3.06 hours.