Question

the number of gallons needed to paint a house depends on the size of the house. suppose N, the number of gallons of paint needed to paint an area of A square feet is given by the formula N=A/250 Find the inverse for this function and explain what the inverse means in the context of the problem.

Answer 1

N will have an inverse because N constantly increases as A does. So, by definition of the inverse, we have\[N(N^{-1}(A))=A=\frac{N^{-1}(A)}{250} \rightarrow N^{-1}(A)=250A\]If N(A) gives you the number of gallons needed to paint a house of area A, \[N^{-1}(A)\]gives you the area that can be painted for a number of gallons, A.

First equation gives says:
"If you know the area to be covered, you can calculate the number of gallons needed."

The second one says:
"If you know the number of gallons, you can calculate the area that can be covered."

Answer 2

Let me know if this explanation is too much or doesn't help.