SOLUTION: This is my last homework problem for the day: New carpeting can be purchased and installed for $22.00 per square yard, plus a $50 delivery fee. (a) Write an equation that gives

Algebra ->  Functions -> SOLUTION: This is my last homework problem for the day: New carpeting can be purchased and installed for $22.00 per square yard, plus a $50 delivery fee. (a) Write an equation that gives       Log On


   

Question 215439: This is my last homework problem for the day:
New carpeting can be purchased and installed for $22.00 per square yard, plus a $50 delivery fee. (a) Write an equation that gives the cost, c, to carpet “s” square yards. (b) Find the inverse of the cost function. © How many square yards can be carpeted for $1810?
Is it C(x)=xs+50 and the inverse is c^-1(x)=x-50/s
80 square yards can be carpeted for $1810
Did I get it right?


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure where the x is coming from?
The equation for the cost (C) of carpeting s square yards at $22.00 per square yard plus %50.00 for delivery would be:
highlight%28C%28s%29+=+22s%2B50%29
To find the inverse of this function, exchange the dependent variable (C) with the independent variable (s) and solve for C.
C+=+22s%2B50 Exchange C and s.
s+=+22C%2B50 Solve this for C. Subtract 50 from both sides.
s-50+=+22C Divide both sides by 22 to get the inverse function C%5E%28-1%29%28s%29
C%5E%28-1%29%28s%29+=+%28s-50%29%2F22
To check to see if you have correct inverse, find the composite of C and C%5E%28-1%29, why? Because C%28C%5E%28-1%29%28s%29%29+=+s if C%5E%28-1%29%28s%29 is the inverse of C%28s%29 :
C%28%28C%5E%28-1%29%29%28s%29%29+=+s
C%28C%5E%28-1%29%29+=+C%28%28s-50%29%2F22%29
C%28%28s-500%29%2F22%29+=+22%28%28s-50%29%2F22%29%2B50=s