The amount of a commodity sold is called the demand for the commodity. The demand D for a certain commodity is a function of the price p given by D(p)=-3p+150.
a) Find D^-1(25)
b) What does your answer represent, in this context?
My work
1. change D(p) to y and p to x
y=-3x+150
2. Swithc x and y
x=-3y+150
3. Solve for y
x-150=-3y -> 3y=-x+150 -> y=(-1/3)x+50
4. Change it back
f^-1(25)=(-1/3)(25)+50 -> f^-1(25)= 41.67
I think i got part a right.
b) What does it represent? If it was in normal form i would say that if the price is 25 than the demand for commodity is 41.67, but since its inverse i dont get it.
a) Find D^-1(25)
b) What does your answer represent, in this context?
My work
1. change D(p) to y and p to x
y=-3x+150
2. Swithc x and y
x=-3y+150
3. Solve for y
x-150=-3y -> 3y=-x+150 -> y=(-1/3)x+50
4. Change it back
f^-1(25)=(-1/3)(25)+50 -> f^-1(25)= 41.67
I think i got part a right.
b) What does it represent? If it was in normal form i would say that if the price is 25 than the demand for commodity is 41.67, but since its inverse i dont get it.
