FUNCTIONS D3

Given that F(x) = 3x  +  11. Find F(-2) – 2F(5)

 

Solution

 

CASE 1: We find F(-2)

 

 

F(x) = 3x  +  11

 

F(-2) = 3(-2)  +  11

 

F(-2) = -6  +  11

 

F(-2) = 5

 

 

Hence  F(-2) = 5

 

 

 

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CASE 2: We find F(5)

 

 

 

F(x) = 3x  +  11

 

F(5) = 3(5)  +  11

 

F(5) = 15  +  11

 

F(5) = 26

 

 

Hence  F(5) = 26

 

 

2F(5) = 2(26) = 52

 

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CASE 3: We find F(-2) – 2F(5)

 

 

= F(-2) – 2F(5)

= 5 – 52

= -47

 

 

TRY THIS………………..

 

 

 

Given that F(x) = 12x  +  78. Find F(-20) – 2F(10)

FUNCTIONS D2

 

LOGARITHMS D1

 

Change the following into Logarithmic form.

i)  4² = 16

ii)  5³ = 125

iii)  3⁰ = 1

Solution

 

 

4² = 16 ⇔ log₄ 16 = 2

5³ = 125 ⇔ log₅ 125 = 3

3⁰ = 1 ⇔ log₃ 1 = 0

TRY THIS………………….

Change the following into Logarithmic form.

i)  7² = 49

ii)  3⁴ = 81

iii)  8⁰ = 1 

FUNCTIONS D1

 

Given that F(x) = 7x  +  11. Find F(-2)

 

Solution

 

F(x) = 7x  +  11

 

F(-2) = 7(-2)  +  11

 

F(-2) = -14  +  11

 

F(-2) = -3

 

 

Hence  F(-2) = -3

 

 

TRY THIS………………..

 

 

Given that F(x) = 16x  +  23. Find F(-3)

CAPACITY D1

 

Change 32.6 liters of water into centiliters

 

Solution

 

1L  =  100cl

32.6L = ?

___________________________  

 

 = 32.6 x  100

           1

 

= 32.6 x 100

 

= 3260cl. Answer

 

 

TRY THIS...................................

 

 

Change 154.3 liters of milk into centiliters

PERFECT SQUARES C1

 

What must be added to x²  + 14x to make the expression a perfect square?

 

Solution

 

a=1, b=14,c=?

 

b² = 4ac

 

(14)² = 4 x 1 x c

 

196 = 4c

196 = 4c

 4       4

 

49 = c

 

Hence number to be added is 49

And the expression will be: x²  + 14x +49=0

 

TRY THIS……………………

What must be added to x²  + 10x to make the expression a perfect square?   

VECTORS C1

 

FACTORIZE C1

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Factorize 1-25m²

 

Solution

 

We use difference of two squares a² – b² = (a - b)(a + b)

 

1-25m² = 1²-5²m²       

 

            = 1² - (5m)²       

 

            = (1 - 5m)(1 + 5m)

 

Hence 1-25m² = (1 - 5m)(1 + 5m)  answer

 

TRY THIS…………….

  

Factorize 1 – 49y²

ALGEBRA C2

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If 12w² = 588; find w.

Solution

12w² = 588

 

12w² = 588               [Dividing by 12 both sides]

12          12

 

w² = 49

w = 7          Because the square root of 49 is 7.   

 

Hence w = 7 . 

 

TRY THIS……………………….

 

If 14u² = 224; find u.

LOGARITHMS C1

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If Log_ax = -20, find Log_a(¹/x⁶)

 

Solution

 

= Log_a(¹/x⁶)                        

 

= Log_ax^-6                   [since ¹/cⁿ =c^-n]

 

= -6 x Log_ax       [since Log_mxⁿ   = nLog_mx]               

 

= -6 x -20

 

= 120

 

TRY THIS………..

 

If Log_aW= -30, find Log_a(¹/W⁵)