Precalculus Math Final Help

Introduction to Precalculus Math Final Help:

The Precalculus is one of the foundation class of mathematics. The topics involved in Precalculus test are real  complex numbers, binomial theorem, composite & polynomial functions, vectors, parametric equations, polar coordinates, matrices, rational functions, solving inequalities & equations and trigonometry. In this article we shall discuss about the examples involved in Precalculus math final help. The following are the examples involved in Precalculus math final help.

Precalculus Math Final Help Problems:

Example 1:  Express the real and imaginary parts for 28 - i `sqrt(14) `

Solution:        Let z= 28 - i `"sqrt(14)`      

Re(z) = 28     Im(z) = `sqrt(14)`

Example 2: For what value of m the vectors `veca` and `vecb` are perpendicular to each other

`veca` =m`veci` + `vecj`` + ``veck`   `vecb`= 7`veci` - 9 `vecj` + 2 `vecj`

Solution: Given `veca` `_|_``vecb `

So, `veca` `vecb` = 0

=> (m`veci` +  `vecj`` + ``veck`) . (7`veci` - 9 `vecj``veck` )

=>  7m - 9 + 2

=>  7m  = 7

m =`7/7`  =1

Example 3: Solve for x,  ln(x-3) + ln(x-2) = ln(2x -6 )

Solution:   Simplify left side, So

ln(x-3) + ln(x-2)= ln(x - 3) (x - 2)

Therefore the given equation can be rewritten as

ln(x - 3)(x - 2) =  ln (2x - 6)

Taking exponent on above equation

eln(x - 3)(x- 2) = eln(2x - 6)

Simplifying the above equation

(x - 3) (x - 2)  = (2x - 6)

x2  - 5x + 6 = 2x - 6

x2  - 7x +12 = 0

Factoring the above equation, we get

(x - 4) (x - 3) = 0

When products of two factors are equal to 0, then one of the factors must be equal to 0.

So, x-4 = 0 => x=4

x-3 = 0 => x=3

Here x = 4 & 3 is the solution.

Example 4:   If f(x) = 14x-1, find f-1(y)?

Solution:Let y = 14x - 1

The given equation can be rewritten as

y + 1 =14x

=> x = y + 1
14

Therefore the f-1(y) = y + 1
14

Example 5: Write the given number in complex form `sqrt(-69)`

Solution: `sqrt(-69)` = `sqrt((-1)(69))`

= `sqrt(-1)` * `sqrt(69)`

= i `sqrt(69)`

Precalculus Math Final Help Practice Problems:

Problem 1:Write the given number in complex form `sqrt(-1415)`

Answer: = i `sqrt(1415)`

Problem 2:Write the real and imaginary parts for 89 - i `sqrt(75) `

Answer:   Re(z) = 89     Im(z) =`sqrt(75)`

Problem 3:   If f(x) = x-9, find f-1(y)?

Answer: y + 9