7. For the function defined by:
f(x)= {x^2, x<=1}
{2x+1, x>1}
a. evaluate f(0)
8. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices.
3x-y=0
5x+2y=22
9. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices
8x-2y=5
-12x+3y=7
10.Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why.
A (3x3) [1st 2, -1, 0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]
B (3x3) [1st 5, 0, 2] [2nd 1, -3, 9] [3rd2, 0, 4]
C (1x1) [1, 3, 5]
1.3A+B
2. B+C
3. CA
11. Given the table below, evaluate the following:
x
-3
-2
-1
0
1
2
3
4
5
f(x)
10
20
30
40
50
60
70
80
90
g(x)
-1
-2
-3
-4
-5
-6
-7
-8
-9
a. (3f+2g(1) b. (fog)(-1)
12. Express the following function, F(x) as a composition of two functions f and g
f(x)= x^2/(x^2+4)
13. You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $25 coupon applied, and g(x) be the price with the 20% discount applied.
a. Write an expression for f(x)
b. Write an expression for g(x)
c. What would the expression (fog)(x) represent?
d. What would the expression (gof)(x) represent?
e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do you know?