Question

The cost (in dollars) of producing a high-end plasma television sets is C = g(x)=700 + 40c. Find a formula for the inverse function g!.9-'(C) =

Answer 1

We are given the function

$C=700+4x$

which we can think of a function that gives us the cost of producing x television sets. The inverse function could be thought as a function that let us know the amount of television sets that we need to produce for us to have a cost C.

To find the inverse function we start by writing the original function

$C=700+4x$

now, we interchange the variables C and x and keep everything else fixed. So we get

$x=700+4C$

now, we want to solve this equation for C. We start by subtracting 700 from both sides, so we get

$x\text{ -700=4C}$

now, we divide both sides by 4. Then, we get

$C=\frac{x\text{ -700}}{4}$

as a matter of notation, we interchange the variables again. So we get

$x=\frac{C\text{ -700}}{4}$

So

$g^{\text{ -1}}(C)=\frac{C\text{ -700}}{4}$