7. A plumbing company installs tankless hot water heaters and charges for both installation time and materials used. a. The heater and supplies cost \( \$ 1800 \) and the shop charges \( \$ 110 / h \)
for a plumber and an apprentice. Write an equation to represent the total cost to the customer. Be sure to state what each variable represents. b. i. What is the slope of the relation? c. Sketch the graph of the relation.
(a) y =110x+1800 where y= total cost and x = no. of hours of work
(b) (i) 110 (ii) 1800
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
