Radical Functions

Inverses

100

Given the following ordered pairs, what are the ordered pairs of the inverse?

(-1,3) , (-2,2),  (4,2), (2,-3)

(3,-1), (2, -2), (2,4), (-3,2)

200

Draw an example of a horizontal line test and write your conclusion.

Is / is not invertible function

300

Find the inverse function of f(x) = sqrt(x-2) + 2

f^-1(x)=x²-4x+6 or f^-1=(x-2)²+2

400

Given f(x)=2x² - 2, what is the inverse of this function?

f^-1(x)=sqrt((x+2)/2)

500

f(x)=2x²-4   and g(x) =sqrt((x+4)/2)

Are f(x) and g(x) inverses? How do you know?

Yes, f(g(x)) and g(f(x)) simplify to x. 

Solving equations

100

sqrt(x) -5= 3

x=64

200

(x-3)^1/2=4x^1/2

x=-1/5

300

3(2x)^1/3 = 6

x=4

400

√(18+7x)=x

x=9

500

sqrt(x+4) - x = 4

x=-4 x=-3

Simplifying Radicals

100

sqrt(16x⁴)

4x²

300

cbrt(8x⁹)

2x²

500

(16x⁸)^1/3

2x²(2x²)^1/3

Radical Algebra

100

4sqrt(3x) + 5sqrt(3x)

9sqrt(3x)

200

2sqrt(x) -3sqrt(2x)

2sqrt(x)-3sqrt(2x)

300

(16x²y⁴/64x⁴y⁴)^1/2

1/2x

400

3sqrt(6x) * 4sqrt(3x²)

36x*sqrt(2x)

500

16√3+4√12-4√48

8√3

Dividing Radicals

100

9√2 / √18

3

200

√6 / √18

√3/3

300

5√12 / √10

√30

400

4 / (√7-4)

(4√7-16)/-9

500

(6+5√3)/(2-√3)

27 + 16√3