Using the function f(x) = 3(x-1) - 0.4(9-x) find each of the following a) f(2) + f(4)
b) f(5)
c) f(7)-f(6)
d) f(3)

a) 7.2 b) 10.4 c) 3.4 d) 3.6

Step-by-step explanation:

f(x) = 3(x - 1) - 0.4(9 - x)

a) f(2) + f(4)

First we will need to find f(2). Substitute 2 for x

f(2) = 3(2 - 1) - 0.4(9 - 2)

Use the distributive property

f(2) = (6 - 3) - (3.6 - 0.8)

f(2) = 3 - 2.8

f(2) = 0.2

Now we need to find f(4). It is the same process as we need for f(2), except x = 4 here

f(4) = 3(4 - 1) - 0.4(9 - 4)

f(4) = (12 - 3) - (3.6 - 1.6)

f(4) = 9 - 2

f(4) = 7

Now we add both answers together:

f(2) + f(4)

0.2 + 7 = 7.2

f(2) + f(4) = 7.2

b) f(5)

f(5) = 3(5 - 1) - 0.4(9 - 5)

f(5) = (15 - 3) - (3.6 - 2)

f(5) = 12 - 1.6

f(5) = 10.4

c) f(7) - f(6)

f(7) = 3(7 - 1) - 0.4(9 - 7)

f(7) = (21 - 3) - (3.6 - 2.8)

f(7) = 18 - 0.8

f(7) = 17.2

f(6) = 3(6 - 1) - 0.4(9 - 6)

f(6) = (18 - 3) - (3.6 - 2.4)

f(6) = 15 - 1.2

f(6) = 13.8

f(7) - f(6)

17.2 - 13.8 = 3.4

f(7) - f(6) = 3.4

d) f(3)

f(3) = 3(3 - 1) - 0.4(9 - 3)

f(3) = (9 - 3) - (3.6 - 1.2)

f(3) = 6 - 2.4

f(3) = 3.6

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: