Can someone help me with my Math homework?

Question

1. Given and evaluate each of the following;

(a)

(b)

(c)

2) (a) Given the following piecewise function:  

                                                

(i) Find  f(−5), f(0), f(8)                                                                                                                          

                  

(ii) Sketch a graph of the function:                                            

 

b) In 2014, ELEC-USA had the following rate schedule for electricity usage for residential purposes;

Monthly service charge $10.00

Per KWh charge:

1st 600 KWh: $0.51/KWh

Over 600 KWh: $1.91/KWh

(i) What is the charge for using 595 KWh in a month?

(ii) What is the charge for using 1550 KWh in a month?

(iii) If C is the monthly charge for x KWh, develop a model relating the monthly charge and kilowatt-hours used. That is, express C as a function of x.

Answer 1

First off:

f(x) = -2x(3x+4)

and for g_inverse

y = -12x-5

x = -12y-5

(X+5) = -12y

(x+5)/-12 = y = g_inverse

1a) Assuming composition:

-2(-12x-5) [ 3*(-12x-5) + 4]

-2(-12x-5) [ -36x - 15 + 4]

2(12x+5)(-36x - 11)

Assuming multiplication:

-2x(3x+4)(-12x+5)

1b) f(1) = -2(1)(3*1+4) = -2(1)(7) = -14

f(-14) = (-2)(-14)(3 * -14 + 4)

= 28(-42+4)

= 28(-38)

= -1064

1c) g_inverse(-5) = 0

2) f(-5) is bot defined

f(0) = 0+5 = 5

f(8) = 4-8 = -4

595 kwh: 10 + 0.51*595 = 313.45

1550 kwh: 10 + 0.51*595 + (1550-600)*1.91

= 313.45 + 950*1.91

= 2127.95

C(x) = 10 + 0.51*x if x<=600;

10 + 0.51x + 1.91*(x-600) otherwise