Mathematics Homework Help

or f(x) = 3×2 + 5 and
g(x) 7x 2 = − ,
a. Verify: g(x + 2) ≠ g(x) + g(2).
b. Find (f – g)(x).
c. Using the resulting function in (b), show that (f – g)(2) = f(2) – g(2).
(The work should be different for each side of the equation.)
d. Is (fg)(0) =
f
g
     
(0)? Explain.2. A size 36 shoe in France is size 3.5 in England. A function that converts shoe sizes
in France to those in England is
3x 94 g(x)
4
−
=
. A size 6 shoe in the United States
is size 3.5 in England. A function that converts shoe sizes in England to those in the
United States is f(x) = x +
5
2
.
a. Use composition of functions to find a function that converts shoe sizes in France to
those in the United States. Simplify the function.
b. Determine the shoe size in the United States for a size 38 shoe in France. Write the answer in
a complete sentence using proper grammar and correct spelling.
3. A dance studio has fixed monthly costs of $1500 that include rent, utilities, insuran