We are given function f(a) = 1.07a for total amount including sales tax.
g(b) = b+50 total cost including delivery.
We need to write function g(f(a)).
g(f(a)) = g of f(a).
We need to substitute function f(a) in g(b) function for b.
g(f(a)) = g(1.07a) = 1.07a +50.
Therefore, g(f(a)) = 1.07a +50.
We are given mattress price a = $1125.
In order to find the total cost including delivery charges, we need to plug a= 1125 in the above function 1.07a +50.
Plugging a= $1125, we get
g(1125) = 1.07a +50 = 1.07*1125 +50 = 1203.75 +50 = 1253.75.
Therefore, total cost including delivery charges is $1253.75.