Chapter 6 Algebra 2

Rational Exponents

100

Simplify

(x^3/4 )(x^9/4)

x³

200

Simplify

(xy³)(x^-4y⁰)

y³x^-3   or y³ / x³

300

Simplify

(27x³)^2/3

9x²

400

Simplify

(xyz)⁰+(xyz)⁰

2

500

Simplify

(5abc)³(2a²b³c⁴)²

500a⁷b⁹c¹⁰

Composition of Functions

100

Find f(g(x))

f(x) = 3x - 4

g(x) = 5x²

15x²-4

200

Find g(f(3))

f(x) = -x² - 2x

g(x) = 2x - 5

-35

300

Find f(g(x))

f(x) = x² - 2x

g(x) = x - 7

x² - 16x + 63

400

Find f^-1(g(x))

f(x) = 6x - 3

g(x) = x - 3

x/6

500

Find f^-1(g^-1(9))

f(x) = x²  (y > 0)

g(x) = x^1/2  (y > 0)

9

Inverse Functions

100

Find the inverse

y = -2x + 8

f^-1(x)= (8-x)/(2)   or  -1/2x + 4

200

Find the inverse

y = x² - 1

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

300

Find the inverse

y = 2x³

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

400

Find the inverse

y = 8

x = 8

500

Find the inverse

y = (3 + x) / (x)

f^-1(x) = (3) / (x-1)

Radical Functions

100

Find the y - intercept

y = (3x)^1/2

y = 0

200

Find the x-intercept.

y = (x-1)^1/2

x = 1

300

Find the y-intercept

y = (x - 5)^1/2

does not exist

400

Find the x-intercept.

y = -6+(2x-5)^1/2

x = 20.5

500

Find the y-intercept.

y = 4 - 3(5x+9)^0.5

-5

Solving Radical Equations

100

Solve

(x+5)^1/2  = 3

x = 4

200

Solve

(x-7)^1/2 - 3 = 4

x = 56

300

Solve

(9x-4)^1/3 = (3x+8)^1/3

x = 2

400

Solve

(x+10)^1/2 + (x-6)^1/2 = 4

x = 6

500

Solve.

(x² - 3x + 12)^1/2 - x - 5 = 0

x = -1