The cost (in dollars) of producing x air conditioners is C=g(x)=560+40x. Find a formula for the inverse function g−1(C).

C = 560 + 40x

inverse: interchange the variables

x = 560 + 40C
C = (x -560)/40 = g^1(C)

7

To find the inverse function of g(x), we need to interchange the roles of x and C and solve for the new variable.

Let's start by rewriting the original equation:
C = 560 + 40x

Interchanging x and C, we get:
x = 560 + 40C

Now, let's solve for C by isolating it:
x - 560 = 40C

Dividing both sides by 40:
C = (x - 560)/40

Therefore, the formula for the inverse function g^(-1)(C) is:
g^(-1)(C) = (C - 560)/40

To find the formula for the inverse function g−1(C), we need to switch the roles of x and C in the original function C=g(x) and solve for x.

The original function is C=g(x)=560+40x.

Step 1: Interchange x and C in the equation: x = 560 + 40C.

Now, we have an equation where x is on the left side and C is on the right side. This equation represents the inverse function g−1(C).

Therefore, the formula for the inverse function g−1(C) is x = 560 + 40C.