PreCalculus Problem Solver

Introduction to Precalculus Problem Solver:

The Precalculus is one of the foundation classes 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 Problem Solver. The following are the examples involved in Precalculus Problem Solver.

Precalculus Problem Solver:

Example 1:  Evaluate the distance between the points (2, 5) and (-1, 2) using distance formula.

Solution :   Given (x1, y1) = (2, 5)

(x2, y2) = (-1, 2)

The distance formula D = `sqrt((x2-x1)^2+(y2-y1)^2)`

= `sqrt((-1-2)^2+(2-5)^2)`

=  `sqrt((-3)^2+(-3)^2)`

= `sqrt(9 + 9)`

= `sqrt(18)`

Example 2:  Express the real and imaginary parts for 19 - i `sqrt(5) `

Solution:        Let z= 19 - i `sqrt(5) `      

Re(z) = 19    Im(z) = `sqrt(5)`

Example 3:   Find the vertex of the parabola y = 2x2 – 16x + 6

Solution:  Given:  y = 2x2 – 16x + 6

We know that x = -`(b)/(2a)` ,

Here a = 2, b = -16

So that,   X =` -b/(2a)` = `-((-16))/(2*2)` = 4

And then y = 2(22) – 16(2) + 6 = 8 – 32 + 6 = -18

So, x = 4 and y = -18.

Example 4:   If f(x) = 7x-1, find f-1(y)?

Solution:Let y = 7x - 1

The given equation can be rewritten as

y + 1 =7x

=> x = y + 1
7

Therefore the f-1(y) = y + 1
7

Example 5: Write the given number in complex form `sqrt(-44)`

Solution: `sqrt(-44)` = `sqrt((-1)(44))`

= `sqrt(-1)` * `sqrt(44)`

= i `sqrt(44)`

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Precalculus Problem Solver:

Problem 1:Write the given number in complex form `sqrt(-175)`

Answer: = i `sqrt(175)`

Problem 2:Write the real and imaginary parts for 22 - i `sqrt(7) `

Answer:   Re(z) = 22    Im(z) =`sqrt(7)`

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

Answer: y + 9

Problem 4: Evaluate distance between the points (4, 5) and (-1, 2) using distance formula.

Answer: D= `sqrt(34)`