I need to write a mathematical expressoin for the function t

I need to write a mathematical expressoin for the function to generate costs of the business for a day.

If running cost of a business is $60 per day plus $3 for each product which is made. The maximum products made in a day is 50.

I also need the domain and range, and the inverse of the function.

Solution

If we take the running cost $60 per day and the cost per unit product is $3 per day, then the cost function C(x) is given by: C(x)=running cost+number units produced*cost per unit of production.So,

C(x) =3*x+60, where x is the number of products manufactured each day.

The domain of x is 0<=x<=50 by the conditions laid down by the problem.

The range of the function C(x) is given by:

0<=C(x)<=50*3+60 or o<=C(x)<=210.

Example: You want to produce 100 units of product on a day. Then the cost ; C(100)= 3*100+60=$360

Inverse function:

Given the cost of a day, the inverse function should give the number of units to be produced.

C(x) = 3x+60

Therefore, x= [C(x)-60]/3. Now replace C(x) by x and x by y to get the inverse function:

y=[x-60]/3 is the inverse of C(x) = 3x+60.

Example:

If 360 is the total cost, to find the number of units to produce, y= (1/3)(360)-20=120-20 =20