6. To host a children's party at an indoor playground, a family pays a non-refundable deposit plus an additional amount for each child attending. If \( 10 \) children attend, the total cost is \( \$ 380 \) . If \( 15 \) children attend, the total cost is \( \$ 440 \) .
(a) Write an equation to relate the total cost, \( C \) , to the number of children attending, \( n . ( 3 \) marks)
C = 12n + 260
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.
