PRE - CALCULUS

EQUATIONS

100

x² + 2x +1 = 3x - 10

x=½ + i√43/2

200

Solve for a, 3/a + a/b= 4b

a= 2b² + √b(4b³ - 3)

300

7y + 5 - 3y + 1= 2y+ 2

y = -2

400

(2x-5)^1/3 = 3

x = 16

500

2t/k - 3 = 8/ k- 2t

t=  = k +√k² + 32 (-k + 3)/ 4

INEQUALITIES

100

2 >= y / 5-1

y = 15

200

3x <= 6

x = 2

300

5(x+2)-3x <= 4+2x+3(x-1)

3 <= x

400

x-3+2 < 10

x<11

500

4x+4/2 > x

-2<x

INVERSE OF A FUNCTION

100

(0,2),(3,4),(-3,-2),(2,4)

Is a function?

This relation is a fuction

200

g(x) = 7x + 18 / 2

g(x) = 2x − 18/ 7

300

g(x)= 4 - 3/2x

f(x)= 1/2x + 3/2

No, they are not inverse

400

g(x)=-2/x - 1

f(x)= -2/x+2

yes, they are inverse

500

 f(x)= (x-2)²

√x + 2 = y

DOMAIN

100

(3x - 2) / (x² - 9)

(-∞, -3)U(-3,3)U(3,∞)

200

√3x+12

[-4,∞)

300

√x² - 16  +5

(-∞,-4] U [4,∞)

400

√x²+9 + √x²-6x

(−∞,0] U [6,∞)

500

√x²−4  + 1 / x³− 27

(−∞,−2] U [2,3) U (3,∞)

FACTORING

100

x² + 3x - 10

(x - 2) (x + 5)

200

x² - 9x + 18

(x - 3) (x - 6)

300

2x² - 5x - 12

(x - 4) (2 x + 3)

400

3x² + 5x + 2

(3x+2)(x+1)

500

8x² - 62x + 99

(4x−9)(2x−11)